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.
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"The author discusses many important topics in the theory of automorphic forms which are rarely seen in the textbooks available on the subject ... the presentation of the proofs ... is ... unusual, and this may give the reader a different flavor of the subject ... graduate students will certainly benefit from this book." -- Mathematical Reviews
"An excellent graduate text. The book by Iwaniec provides the graduate student and the researcher wishing to acquire the basics on automorphic forms with a beautifully written and self-contained treatment of the classical modular and automorphic forms, Kloosterman sums, Hecke operators, automorphic L-functions, cusp forms and Eisenstein series, spherical functions, theta functions and convolution L-functions." -- Bulletin of the London Mathematical Society
"An excellent place to begin the study of the analytic approach to modular forms ... a welcome addition to this growing expository of literature." -- Bulletin of the American Mathematical Society
"[T]his is an excellent book, requiring hard work from the reader and giving rich reward for her or his effort." -- Zentralblatt fur Mathematik
"An excellent graduate text. The book by Iwaniec provides the graduate student and the researcher wishing to acquire the basics on automorphic forms with a beautifully written and self-contained treatment of the classical modular and automorphic forms, Kloosterman sums, Hecke operators, automorphic L-functions, cusp forms and Eisenstein series, spherical functions, theta functions and convolution L-functions." -- Bulletin of the London Mathematical Society
"An excellent place to begin the study of the analytic approach to modular forms ... a welcome addition to this growing expository of literature." -- Bulletin of the American Mathematical Society
"[T]his is an excellent book, requiring hard work from the reader and giving rich reward for her or his effort." -- Zentralblatt fur Mathematik
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1 of 8 people found the following review helpful:
5.0 out of 5 stars
A top book in operator algebra,
By shamooshaky (Iran) - See all my reviews
This review is from: Fundamentals of the theory of operator algebras. V2, Volume 100-II: Advanced theory (Pure and Applied Mathematics) (Hardcover)
This book contain 14 Chapter in 2 volume. In v.1 the authours detailed the elementary property of operators and operator algebra in Hilbert spaces. In volume 2 the authours investigate more advance results and detail on some concepts such as cross product and direct integral of Hilbert spaces.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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tracial weight, modular condition relative, generating trace vector, completely additive state, unit generating vector, csm space, matricial algebras, corresponding modular automorphism group, generating nest, unitary implementation theorem, normal product states, reduced atomic representation, central subprojection, central linear functional, decomposable projection, preclosed operators, ultraweak continuity, ultraweak closure, equivalent abelian projections, maximal orthogonal family, ultraweakly continuous linear functional, automorphism group corresponding, positive linear mapping, infinite orthogonal family, numerical trace Key Phrases - Capitalized Phrases (CAPs): (learn more)
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tracial weight, modular condition relative, generating trace vector, completely additive state, unit generating vector, csm space, matricial algebras, corresponding modular automorphism group, generating nest, unitary implementation theorem, normal product states, reduced atomic representation, central subprojection, central linear functional, decomposable projection, preclosed operators, ultraweak continuity, ultraweak closure, equivalent abelian projections, maximal orthogonal family, ultraweakly continuous linear functional, automorphism group corresponding, positive linear mapping, infinite orthogonal family, numerical trace Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 7
books:
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- Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos in Back Matter
- Operator Algebras in Dynamical Systems (Encyclopedia of Mathematics and its Applications) by Shtichirt Sakai in Front Matter
- Real and Complex Analysis (International Series in Pure and Applied Mathematics) by Walter Rudin in Back Matter
- General Topology (Graduate Texts in Mathematics) by John L. Kelley in Back Matter
- Noncommutative Geometry by Alain Connes in Front Matter
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