Fundamentals of the Theory of Operator Algebras. Volume I ：Elementary Theory ( Graduate Studies in Mathematics )

Publication subTitle ：Elementary Theory

Publication series ：Graduate Studies in Mathematics

Author： Richard V. Kadison;John R. Ringrose  

Publisher： American Mathematical Society‎

Publication year： 1997

E-ISBN: 9781470420727

P-ISBN(Paperback): 9780821808191

Subject： O177 functional analysis

Keyword： Analysis

Language： ENG

Access to resources Favorite

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Fundamentals of the Theory of Operator Algebras. Volume I

Description

This book, together with Fundamentals of the Theory of Operator Algebras. Volume II, Advanced Theory, Graduate Studies in Mathematics, vol. 16, 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. The book is intended for graduate students and research mathematicians, and mathematical physicists interested in functional analysis, operator algebras, and applications. It can also be used as a text for a graduate course in any of these areas. 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 Lo

Chapter

Cover

Title

Copyright

Contents

Preface

Contents of Volume II

Chapter 1. Linear Spaces

1.1. Algebraic results

1.2. Linear topological spaces

1.3. Weak topologies

1.4. Extreme points

1.5. Normed spaces

1.6. Linear functionals on normed spaces

1.7. Some examples of Banach spaces

1.8. Linear operators acting on Banach spaces

1.9.Exercises

Chapter 2. Basics of Hilbert Space and Linear Operators

2.1. Inner products on linear spaces

2.2. Orthogonality

2.3. The weak topology

2.4. Linear operators

General theory

Classes of operators

2.5. The lattice of projections

2.6. Constructions with Hilbert spaces

Subspaces

Direct sums

Tensor products and the Hilbert–Schmidt class

Matrix representations

2.7. Unbounded linear operators

2.8. Exercises

Chapter 3. Banach Algebras

3.1. Basics

3.2. The spectrum

The Banach algebra L[sub(1)](R) and Fourier analysis

3.3. The holomorphic function calculus

Holomorphic functions

The holomorphic function calculus

3.4. The Banach algebra C(X)

3.5. Exercises

Chapter 4. Elementary C*-Algebra Theory

4.1. Basics

4.2. Order structure

4.3. Positive linear functionals

4.4. Abelian algebras

4.5. States and representations

4.6. Exercises

Chapter 5. Elementary von Neumann Algebra Theory

5.1. The weak- and strong- operator topologies

5.2. Spectral theory for bounded operators

5.3. Two fundamental approximation theorems

5.4. Irreducible algebras—an application

5.5. Projection techniques and constructs

Central carriers

Some constructions

Cyclicity, separation, and countable decomposability

5.6. Unbounded operators and abelian von Neumann algebras

5.7. Exercises

Bibliography

Index of Notation

Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

The users who browse this book also browse


No browse record.