Introduction to operator space theory:
The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
|
| Schriftenreihe: | London Mathematical Society lecture note series
294 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of 'length' of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (vii, 478 pages) |
| ISBN: | 9781107360235 |
| DOI: | 10.1017/CBO9781107360235 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941703 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9781107360235 |c Online |9 978-1-107-36023-5 | ||
| 024 | 7 | |a 10.1017/CBO9781107360235 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781107360235 | ||
| 035 | |a (OCoLC)992827383 | ||
| 035 | |a (DE-599)BVBBV043941703 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 515/.732 |2 21 | |
| 084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 100 | 1 | |a Pisier, Gilles |d 1950- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to operator space theory |c Gilles Pisier |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2003 | |
| 300 | |a 1 online resource (vii, 478 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a London Mathematical Society lecture note series |v 294 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises | |
| 520 | |a The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of 'length' of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer | ||
| 650 | 4 | |a Operator spaces | |
| 650 | 0 | 7 | |a Operatorraum |0 (DE-588)4591231-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Operatorraum |0 (DE-588)4591231-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-81165-1 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9781107360235 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350673 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9781107360235 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9781107360235 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176883787497472 |
|---|---|
| any_adam_object | |
| author | Pisier, Gilles 1950- |
| author_facet | Pisier, Gilles 1950- |
| author_role | aut |
| author_sort | Pisier, Gilles 1950- |
| author_variant | g p gp |
| building | Verbundindex |
| bvnumber | BV043941703 |
| classification_rvk | SI 320 SK 620 |
| collection | ZDB-20-CBO |
| contents | Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises |
| ctrlnum | (ZDB-20-CBO)CR9781107360235 (OCoLC)992827383 (DE-599)BVBBV043941703 |
| dewey-full | 515/.732 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.732 |
| dewey-search | 515/.732 |
| dewey-sort | 3515 3732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107360235 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03854nmm a2200481zcb4500</leader><controlfield tag="001">BV043941703</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107360235</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-107-36023-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9781107360235</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781107360235</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)992827383</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941703</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.732</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pisier, Gilles</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to operator space theory</subfield><subfield code="c">Gilles Pisier</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (vii, 478 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">London Mathematical Society lecture note series</subfield><subfield code="v">294</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of 'length' of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator spaces</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Operatorraum</subfield><subfield code="0">(DE-588)4591231-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Operatorraum</subfield><subfield code="0">(DE-588)4591231-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-81165-1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781107360235</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350673</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781107360235</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781107360235</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043941703 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781107360235 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350673 |
| oclc_num | 992827383 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (vii, 478 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Pisier, Gilles 1950- Verfasser aut Introduction to operator space theory Gilles Pisier Cambridge Cambridge University Press 2003 1 online resource (vii, 478 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 294 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C*-algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of 'length' of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer Operator spaces Operatorraum (DE-588)4591231-2 gnd rswk-swf Operatorraum (DE-588)4591231-2 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-81165-1 https://doi.org/10.1017/CBO9781107360235 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pisier, Gilles 1950- Introduction to operator space theory Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises Operator spaces Operatorraum (DE-588)4591231-2 gnd |
| subject_GND | (DE-588)4591231-2 |
| title | Introduction to operator space theory |
| title_auth | Introduction to operator space theory |
| title_exact_search | Introduction to operator space theory |
| title_full | Introduction to operator space theory Gilles Pisier |
| title_fullStr | Introduction to operator space theory Gilles Pisier |
| title_full_unstemmed | Introduction to operator space theory Gilles Pisier |
| title_short | Introduction to operator space theory |
| title_sort | introduction to operator space theory |
| topic | Operator spaces Operatorraum (DE-588)4591231-2 gnd |
| topic_facet | Operator spaces Operatorraum |
| url | https://doi.org/10.1017/CBO9781107360235 |
| work_keys_str_mv | AT pisiergilles introductiontooperatorspacetheory |