Real operator algebras /

Real operator algebras /

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Bibliographic Details
Author / Creator:Li, Bingren, 1941-
Imprint:River Edge, N.J. : World Scientific, ©2003.
Description:1 online resource (xiii, 241 pages)
Language:English
Subject:
Banach algebras.
Operator algebras.
Banach algebras.
Operator algebras.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11169978
Hidden Bibliographic Details
Other authors / contributors:Li, Bingren, 1941-
ISBN:9789812795182
9812795189
1281935611
9781281935618
9812383808
9789812383808
Notes:Includes bibliographical references (pages 233-235) and indexes.
Print version record.
Summary:The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently. The aim of this text is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras.
Other form:Print version: Li, Bing₉ren, 1941- Real operator algebras. River Edge, N.J. : World Scientific, ©2003 9812383808
Table of Contents:
  • 1. Real Banach and Hilbert spaces. 1.1. Complexification of real Banach and Hilbert spaces. 1.2. Spectral decomposition theorem in real Hilbert spaces
  • 2. Real Banach algebras. 2.1. Definition and complexification. 2.2. Divisible real Banach algebras. 2.3. The topological group of invertible elements and its principal component. 2.4. Radical. 2.5. Functional calculus. 2.6. Arens products. 2.7. Abelian real Banach algebras
  • 3. Real Banach * algebras. 3.1. Some basic lemmas. 3.2. Abelian real Banach * algebras. 3.3. Positive linear functionals and GNS construction. 3.4. * Representations and topologically irreducible * representations. 3.5. * Radical. 3.6. Symmetric real Banach * algebras
  • 4. Fundamentals of real Von Neumann algebras. 4.1. Banach spaces of operators on a real Hilbert space. 4.2. Locally convex topologies in B(H). 4.3. Von Neumann's double commutation theorem. 4.4. Kaplansky's density theorem, tensor product commutation theorem, and comparison of projections. 4.5. Positive linear functionals. 4.6. [symbol]-finite real VN algebras
  • 5. Fundamentals of real C*-algebras. 5.1. Definition and basic properties. 5.2. Positive functionals and equivalent definition of real C*-algebras. 5.3. Pure real states, their left kernels, and irreducible * representations. 5.4. Ideals, quotient algebras and extreme points. 5.5. The bidual of a real C*-algebra. 5.6. The uniqueness of * operation. 5.7. Finite-dimensional real C*-algebras. 5.8. The enveloping real C*-algebra of a hermitian real Banach * algebra. 5.9. * Representations of abelian real C*-algebras
  • 6. Real W*-algebras. 6.1. Definition and basic properties. 6.2. Normal linear functionals and singular linear functionals. 6.3. Abelian real W*-algebras. 6.4. Unitaries and partial isometries
  • 7. Gelfand-Naimark conjecture in the real case. 7.1. Real C*-equivalent algebras. 7.2. The closed unit ball of a unital real C*-algebra. 7.3. Gelfand-Naimark conjecture in the real case
  • 8. Classification of real W*-algebras. 8.1. Classification of real W*-algebras. 8.2. Finite real W*-algebras. 8.3. Properly infinite real W*-algebras. 8.4. Semi-finite real W*-algebras. 8.5. Purely infinite (type III) real W*-algebras. 8.6. Properties on other classes of real W*-algebras. 8.7. Real factors and tensor products
  • 9. Real reduction theory. 9.1. Real measurable fields of Hilbert spaces. 9.2. Real measurable fields of operators. 9.3. Real measurable fields of VN algebras. 9.4. Real reduction theory
  • 10. (AF) real C*-algebras. 10.1. Standard matrix unit. 10.2. Technical lemmas. 10.3. Definition and basic properties.

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