Finite von Neumann algebras and masas:
A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2008
|
| Schriftenreihe: | London Mathematical Society lecture note series
351 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa's methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of a II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (ix, 400 pages) |
| ISBN: | 9780511666230 |
| DOI: | 10.1017/CBO9780511666230 |
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| 245 | 1 | 0 | |a Finite von Neumann algebras and masas |c Allan M. Sinclair, Roger R. Smith |
| 246 | 1 | 3 | |a Finite von Neumann Algebras & Masas |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a General introduction -- Masas in B(H) -- Finite von Neumann algebras -- The basic construction -- Projections and partial isometries -- Normalisers, orthogonality, and distances -- The Pukanszky invariant -- Operators in L -- Perturbations -- General perturbations -- Singular masas -- Existence of special masas -- Irreducible hyperfinite subfactors -- Maximal injective subalgebras -- Masas in non-separable factors -- Singly generated II1 factors -- Appendix A. The ultrapower and property GAMMA -- Appendix B. Unbounded operators -- Appendix C -- The trace revisited -- Index | |
| 520 | |a A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa's methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of a II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Sinclair, Allan M. |
| author_facet | Sinclair, Allan M. |
| author_role | aut |
| author_sort | Sinclair, Allan M. |
| author_variant | a m s am ams |
| building | Verbundindex |
| bvnumber | BV043941918 |
| classification_rvk | SI 320 SK 600 |
| collection | ZDB-20-CBO |
| contents | General introduction -- Masas in B(H) -- Finite von Neumann algebras -- The basic construction -- Projections and partial isometries -- Normalisers, orthogonality, and distances -- The Pukanszky invariant -- Operators in L -- Perturbations -- General perturbations -- Singular masas -- Existence of special masas -- Irreducible hyperfinite subfactors -- Maximal injective subalgebras -- Masas in non-separable factors -- Singly generated II1 factors -- Appendix A. The ultrapower and property GAMMA -- Appendix B. Unbounded operators -- Appendix C -- The trace revisited -- Index |
| ctrlnum | (ZDB-20-CBO)CR9780511666230 (OCoLC)851004123 (DE-599)BVBBV043941918 |
| dewey-full | 512/.556 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.556 |
| dewey-search | 512/.556 |
| dewey-sort | 3512 3556 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511666230 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511666230 |
| language | English |
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| spelling | Sinclair, Allan M. Verfasser aut Finite von Neumann algebras and masas Allan M. Sinclair, Roger R. Smith Finite von Neumann Algebras & Masas Cambridge Cambridge University Press 2008 1 online resource (ix, 400 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 351 Title from publisher's bibliographic system (viewed on 05 Oct 2015) General introduction -- Masas in B(H) -- Finite von Neumann algebras -- The basic construction -- Projections and partial isometries -- Normalisers, orthogonality, and distances -- The Pukanszky invariant -- Operators in L -- Perturbations -- General perturbations -- Singular masas -- Existence of special masas -- Irreducible hyperfinite subfactors -- Maximal injective subalgebras -- Masas in non-separable factors -- Singly generated II1 factors -- Appendix A. The ultrapower and property GAMMA -- Appendix B. Unbounded operators -- Appendix C -- The trace revisited -- Index A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa's methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of a II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory Von Neumann algebras VonNeumann-Algebra (DE-588)4388395-3 gnd rswk-swf VonNeumann-Algebra (DE-588)4388395-3 s 1\p DE-604 Smith, Roger R. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-71919-3 https://doi.org/10.1017/CBO9780511666230 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sinclair, Allan M. Finite von Neumann algebras and masas General introduction -- Masas in B(H) -- Finite von Neumann algebras -- The basic construction -- Projections and partial isometries -- Normalisers, orthogonality, and distances -- The Pukanszky invariant -- Operators in L -- Perturbations -- General perturbations -- Singular masas -- Existence of special masas -- Irreducible hyperfinite subfactors -- Maximal injective subalgebras -- Masas in non-separable factors -- Singly generated II1 factors -- Appendix A. The ultrapower and property GAMMA -- Appendix B. Unbounded operators -- Appendix C -- The trace revisited -- Index Von Neumann algebras VonNeumann-Algebra (DE-588)4388395-3 gnd |
| subject_GND | (DE-588)4388395-3 |
| title | Finite von Neumann algebras and masas |
| title_alt | Finite von Neumann Algebras & Masas |
| title_auth | Finite von Neumann algebras and masas |
| title_exact_search | Finite von Neumann algebras and masas |
| title_full | Finite von Neumann algebras and masas Allan M. Sinclair, Roger R. Smith |
| title_fullStr | Finite von Neumann algebras and masas Allan M. Sinclair, Roger R. Smith |
| title_full_unstemmed | Finite von Neumann algebras and masas Allan M. Sinclair, Roger R. Smith |
| title_short | Finite von Neumann algebras and masas |
| title_sort | finite von neumann algebras and masas |
| topic | Von Neumann algebras VonNeumann-Algebra (DE-588)4388395-3 gnd |
| topic_facet | Von Neumann algebras VonNeumann-Algebra |
| url | https://doi.org/10.1017/CBO9780511666230 |
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