Fundamentals of the theory of operator algebras

著者

• Kadison, Richard V.
• Ringrose, John R

書誌事項

Fundamentals of the theory of operator algebras

Richard V. Kadison, John R. Ringrose

（Graduate studies in mathematics, v. 15-16）

American Mathematical Society, c1997

• v. 1
• v. 2

注記

Second printing, incorporating minor corrections, of the work originally published: New York : Academic Press, 1983. (Pure and applied mathematics (Academic Press) ; 100)

Vol. 1. Elementary theory -- v. 2. Advanced theory

Includes bibliographies and indexes

内容説明・目次

巻冊次

v. 1 ISBN 9780821808191

内容説明

This work and ""Fundamentals of the Theory of Operator Algebras Volume II, Advanced Theory"" present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology.The book presents the possibility for the design of numerous courses aimed at different audiences. '...these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory' - ""Bulletin of the London Mathematical Society"". 'Volumes I and II were published in 1982 and 1983. Since then they have quickly established themselves as The Textbooks in operator algebra theory'- ""Bulletin of the American Mathematical Society"". 'One of the splendid features of the original two volumes is their large supply of exercises...which illustrate the results of the text and expand its scope' - ""L'Enseignement Mathematique"".

目次

Linear spaces Basics of Hilbert space and linear operators Banach algebras Elementary $C^*$-algebra theory Elementary von Neumann algebra theory Bibliography Index of notation Index.

巻冊次

v. 2 ISBN 9780821808207

内容説明

This work and ""Fundamentals of the Theory of Operator Algebras, Volume I, Elementary Theory"" present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology.The book presents the possibility for the design of numerous courses aimed at different audiences. '...these two volumes represent a magnificent achievement. They will be an essential item on every operator algebraist's bookshelves and will surely become the primary source of instruction for research students in von Neumann algebra theory' - ""Bulletin of the London Mathematical Society"". 'Volumes I and II were published in 1982 and 1983. Since then they have quickly established themselves as The Textbooks in operator algebra theory' - ""Bulletin of the American Mathematical Society"". 'One of the splendid features of the original two volumes is their large supply of exercises...which illustrate the results of the text and expand its scope' - ""L'Enseignement Mathematique"".

目次

Comparison theory of projection Normal states and unitary equivalence of von Neumann algebras The trace Algebra and commutant Special representation of $C^*$-algebras Tensor products Approximation by matrix algebras Crossed products Direct integrals and decompositions Bibliography Index of notation Index.

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詳細情報

• NII書誌ID(NCID): BA32186853
• ISBN:
  • 9780821808191
  • 9780821808207
• LCCN: 97020916
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: 2 v. (xv, 1074 p.)
• 大きさ: 27 cm
• 分類:
  • LCC : QA326
  • DC21 : 512/.55
  • NDC8 : 411.72
• 件名:
  • LCSH : Operator algebras
• 親書誌ID:
  • BA20542214