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Book DetailsGraduate Studies in MathematicsVolume: 15; 1997; 398 ppMSC: Primary 46; Secondary 47The return of a classic!
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.
Praise for both volumes ...
“ ... 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 mathématique
ReadershipGraduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.
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Table of Contents
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Chapters
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Chapter 1. Linear spaces
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Chapter 2. Basics of Hilbert space and linear operators
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Chapter 3. Banach algebras
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Chapter 4. Elementary $C^*$-algebra theory
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Chapter 5. Elementary von Neumann algebra theory
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Reviews
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Drawing on their rich experience, the authors have succeeded in presenting a very attractive and well-written book that conveys the flavor and the beauty of classical operator algebra theory and that should be ideally suited as a text for a graduate course on the subject.
Zentralblatt MATH -
The authors have presented it [the material] in a fresh and attractive way which conveys the spirit and beauty of the subject ... a beautiful book.
Mathematical Reviews -
Most of Volume I is devoted to three chapters of preparatory material. In fact, these chapters form a general introduction to functional analysis which could hardly be bettered.
Bulletin of the London Mathematical Society
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
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.
Praise for both volumes ...
“ ... 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 mathématique
Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.
-
Chapters
-
Chapter 1. Linear spaces
-
Chapter 2. Basics of Hilbert space and linear operators
-
Chapter 3. Banach algebras
-
Chapter 4. Elementary $C^*$-algebra theory
-
Chapter 5. Elementary von Neumann algebra theory
-
Drawing on their rich experience, the authors have succeeded in presenting a very attractive and well-written book that conveys the flavor and the beauty of classical operator algebra theory and that should be ideally suited as a text for a graduate course on the subject.
Zentralblatt MATH -
The authors have presented it [the material] in a fresh and attractive way which conveys the spirit and beauty of the subject ... a beautiful book.
Mathematical Reviews -
Most of Volume I is devoted to three chapters of preparatory material. In fact, these chapters form a general introduction to functional analysis which could hardly be bettered.
Bulletin of the London Mathematical Society
