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.
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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
"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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This chapter contains an account of those basic aspects of linear functional analysis that are needed, later in the book, in the study of operator algebras. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
holomorphic function calculus, bounded multilinear functional, bounding projection, boundedly complete lattice, pure state space, bounding sequence, decomposable relative, hermitian linear functionals, right approximate identity, finite subsums, hermitian functionals, closed left ideal, algebraic dual space, multiplicative linear functional, meager set, cyclic projection, dense linear manifold, clopen set, adjoint subspace, algebra acting, double commutant theorem, uniqueness clause, simple tensors, bounded linear operator acting, clopen subset Key Phrases - Capitalized Phrases (CAPs): (learn more)
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This chapter contains an account of those basic aspects of linear functional analysis that are needed, later in the book, in the study of operator algebras. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
holomorphic function calculus, bounded multilinear functional, bounding projection, boundedly complete lattice, pure state space, bounding sequence, decomposable relative, hermitian linear functionals, right approximate identity, finite subsums, hermitian functionals, closed left ideal, algebraic dual space, multiplicative linear functional, meager set, cyclic projection, dense linear manifold, clopen set, adjoint subspace, algebra acting, double commutant theorem, uniqueness clause, simple tensors, bounded linear operator acting, clopen subset Key Phrases - Capitalized Phrases (CAPs): (learn more)
Use Proposition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
books:
66
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cite this book:
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- General Topology (Undergraduate Texts in Mathematics) by J. Dixmier in Back Matter
- Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos in Back 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
- Mappings of Operator Algebras (Progress in Mathematics) by H. Araki on page 109, and page 304
- Current Research in Operational Quantum Logic: Algebras, Categories, Languages (Fundamental Theories of Physics) by Bob Coecke on page 243, and page 261
- Analyse mathématique IV: Intégration et théorie spectrale, analyse harmonique, le jardin des délices modulaires (French Edition) by Roger Godement on page 141, and page 177
- From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics (Oxford Logic Guides) by Laura Crosilla on page 292, and page 303
- From Micro to Macro Quantum Systems: A Unified Formalism With Superselection Rules And Its Applications by K. Kong Wan on page 227, and Back Matter
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