Geometric Functional Analysis and its Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1975
|
| Schriftenreihe: | Graduate Texts in Mathematics
24 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its applications. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the HahnBanach principle, the latter appearing in ten different but equivalent formulations (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces |
| Beschreibung: | 1 Online-Ressource (X, 246 p) |
| ISBN: | 9781468493696 9781468493719 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9369-6 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421206 | ||
| 003 | DE-604 | ||
| 005 | 20180109 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1975 |||| o||u| ||||||eng d | ||
| 020 | |a 9781468493696 |c Online |9 978-1-4684-9369-6 | ||
| 020 | |a 9781468493719 |c Print |9 978-1-4684-9371-9 | ||
| 024 | 7 | |a 10.1007/978-1-4684-9369-6 |2 doi | |
| 035 | |a (OCoLC)863995185 | ||
| 035 | |a (DE-599)BVBBV042421206 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Holmes, Richard B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric Functional Analysis and its Applications |c by Richard B. Holmes |
| 264 | 1 | |a New York, NY |b Springer New York |c 1975 | |
| 300 | |a 1 Online-Ressource (X, 246 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Graduate Texts in Mathematics |v 24 |x 0072-5285 | |
| 500 | |a This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its applications. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the HahnBanach principle, the latter appearing in ten different but equivalent formulations (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Konvexität |0 (DE-588)4114284-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | 1 | |a Geometrie |0 (DE-588)4020236-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Konvexität |0 (DE-588)4114284-6 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 830 | 0 | |a Graduate Texts in Mathematics |v 24 |w (DE-604)BV000000067 |9 24 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4684-9369-6 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856623 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153094005587968 |
|---|---|
| any_adam_object | |
| author | Holmes, Richard B. |
| author_facet | Holmes, Richard B. |
| author_role | aut |
| author_sort | Holmes, Richard B. |
| author_variant | r b h rb rbh |
| building | Verbundindex |
| bvnumber | BV042421206 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863995185 (DE-599)BVBBV042421206 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9369-6 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03437nmm a2200529zcb4500</leader><controlfield tag="001">BV042421206</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180109 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1975 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468493696</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4684-9369-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468493719</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4684-9371-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4684-9369-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863995185</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421206</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Holmes, Richard B.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometric Functional Analysis and its Applications</subfield><subfield code="c">by Richard B. Holmes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1975</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 246 p)</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="1" ind2=" "><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">24</subfield><subfield code="x">0072-5285</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its applications. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the HahnBanach principle, the latter appearing in ten different but equivalent formulations (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexität</subfield><subfield code="0">(DE-588)4114284-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</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="689" ind1="1" ind2="0"><subfield code="a">Konvexität</subfield><subfield code="0">(DE-588)4114284-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">24</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">24</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4684-9369-6</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856623</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="883" ind1="1" ind2=" "><subfield code="8">2\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></record></collection> |
| id | DE-604.BV042421206 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468493696 9781468493719 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856623 |
| oclc_num | 863995185 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 246 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Springer New York |
| record_format | marc |
| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Holmes, Richard B. Verfasser aut Geometric Functional Analysis and its Applications by Richard B. Holmes New York, NY Springer New York 1975 1 Online-Ressource (X, 246 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 24 0072-5285 This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its applications. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the HahnBanach principle, the latter appearing in ten different but equivalent formulations (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces Mathematics Mathematics, general Mathematik Geometrie (DE-588)4020236-7 gnd rswk-swf Konvexität (DE-588)4114284-6 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s Geometrie (DE-588)4020236-7 s 1\p DE-604 Konvexität (DE-588)4114284-6 s 2\p DE-604 Graduate Texts in Mathematics 24 (DE-604)BV000000067 24 https://doi.org/10.1007/978-1-4684-9369-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Holmes, Richard B. Geometric Functional Analysis and its Applications Graduate Texts in Mathematics Mathematics Mathematics, general Mathematik Geometrie (DE-588)4020236-7 gnd Konvexität (DE-588)4114284-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4114284-6 (DE-588)4018916-8 |
| title | Geometric Functional Analysis and its Applications |
| title_auth | Geometric Functional Analysis and its Applications |
| title_exact_search | Geometric Functional Analysis and its Applications |
| title_full | Geometric Functional Analysis and its Applications by Richard B. Holmes |
| title_fullStr | Geometric Functional Analysis and its Applications by Richard B. Holmes |
| title_full_unstemmed | Geometric Functional Analysis and its Applications by Richard B. Holmes |
| title_short | Geometric Functional Analysis and its Applications |
| title_sort | geometric functional analysis and its applications |
| topic | Mathematics Mathematics, general Mathematik Geometrie (DE-588)4020236-7 gnd Konvexität (DE-588)4114284-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Geometrie Konvexität Funktionalanalysis |
| url | https://doi.org/10.1007/978-1-4684-9369-6 |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT holmesrichardb geometricfunctionalanalysisanditsapplications |