Theory of operator algebras
著者
書誌事項
Theory of operator algebras
(Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 124-125,
Springer, c2002-c2003
- 1
- 2
- 3
- 3 : softcover
- タイトル別名
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Theory of operator algebra
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注記
"2nd printing of the first edition 1979, which was originally published as Theory of Operator Algebras I, ISBN 0-387-90391-7"--T.p. verso of I
"Softcover reprint of the hardcover 1st edition 2003"--T.p. of v. 3 of softcover
Bibliography: 1, p. 387-407. 2, p. [491]-508. 3, p. [523]-540
Includes indexes
内容説明・目次
- 巻冊次
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1 ISBN 9783540422488
内容説明
Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.
目次
Fundaments of Banach Algebras and C*-Algebras.- Topologies and Density Theorems in Operator Algebras.- Conjugate Spaces.- Tensor Products of Operator Algebras and Direct Integrals.- Types of von Neumann Algebras and Traces.- Appendix: Polish Spaces and Standard Borel Spaces.
- 巻冊次
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3 ISBN 9783540429135
内容説明
From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." Acta Scientiarum Mathematicarum
目次
XIII Ergodic Transformation Groups and the Associated von Neumann Algebras.- XIV Approximately Finite Dimensional von Neumann Algebras.- XV Nuclear C*-Algebras.- XVI Injective von Neumann Algebras.- XVII Non-Commutative Ergodic Theory.- XVIII Structure of Approximately Finite Dimensional Factors.- XIX Subfactors of an Approximately Finite Dimensional Factor of Type II1.- Notation Index.
- 巻冊次
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2 ISBN 9783540429142
内容説明
Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis.
From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM
目次
VI Left Hilbert Algebras.- VII Weights.- VIII Modular Automorphism Groups.- IX Non-Commutative Integration.- X Crossed Products and Duality.- XI Abelian Automorphism Group.- XII Structure of a von Neumann Algebra of Type III.- Notation Index.
- 巻冊次
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3 : softcover ISBN 9783642076886
内容説明
From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." Acta Scientiarum Mathematicarum
目次
XIII Ergodic Transformation Groups and the Associated von Neumann Algebras.- XIV Approximately Finite Dimensional von Neumann Algebras.- XV Nuclear C*-Algebras.- XVI Injective von Neumann Algebras.- XVII Non-Commutative Ergodic Theory.- XVIII Structure of Approximately Finite Dimensional Factors.- XIX Subfactors of an Approximately Finite Dimensional Factor of Type II1.- Notation Index.
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