Theory of operator algebras

Author(s)

• 竹崎, 正道 タケサキ, マサミチ

Bibliographic Information

Theory of operator algebras

M. Takesaki

（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 124-125, 127 . Operator algebras and non-commutative geometry ; 5-6, 8）

Springer, c2002-c2003

• 1
• 2
• 3
• 3 : softcover

Other Title

Theory of operator algebra

Note

"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

Description and Table of Contents

Volume

1 ISBN 9783540422488

Description

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.

Table of Contents

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.

Volume

3 ISBN 9783540429135

Description

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

Table of Contents

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.

Volume

2 ISBN 9783540429142

Description

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

Table of Contents

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.

Volume

3 : softcover ISBN 9783642076886

Description

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

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BA54619218
• ISBN:
  • 354042248X
  • 354042914X
  • 3540429131
  • 9783642076886
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: 3 v.
• Size: 25 cm
• Subject Headings:
  • LCSH : Operator algebras
• Parent Bibliography ID:
  • BA01321819