Real Operator Algebras

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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 book is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras, real C-algebras and W-algebras, etc.), and some basic facts are given, one can get some results on real operator algebras easily.

The book is also an introduction to real operator algebras, written in a self-contained manner. The reader needs just a general knowledge of Banach algebras and operator algebras.

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Product Details

  • ISBN-13: 9789812383808
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 5/28/2003
  • Pages: 256
  • Product dimensions: 6.10 (w) x 9.10 (h) x 0.80 (d)

Table of Contents

1 Real Banach and Hilbert Spaces 1
2 Real Banach Algebras 15
3 Real Banach * Algebras 37
4 Fundamentals of Real Von Neumann Algebras 59
5 Fundamentals of Real C[superscript *]-Algebras 77
6 Real W[superscript *]-Algebras 123
7 Gelfand-Naimark Conjecture in the Real Case 147
8 Classification of Real W[superscript *]-Algebras 167
9 Real Reduction Theory 191
10 (AF) Real C[superscript *]-Algebras 211
Bibliography 233
Notation Index 237
Index 239
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