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Other titles in the Lecture Notes in Mathematics series:

Lecture Notes in Mathematics, #1711: Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

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Synopses & Reviews

Publisher Comments:

This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra of projections. One of the main aims is to employ the methods of vector measures and integration as a unifying theme throughout. This yields proofs of several classical results which are quite different to the classical ones. This book is directed to both those wishing to learn this topic for the first time and to current experts in the field.

Description:

Includes bibliographical references (p. [121]-123) and index.

Table of Contents

Preface.- Introduction.- Vector measures and Banach spaces.- Abstract Boolean algebras and Stone spaces.- Boolean algebras of projections and uniformly closed operator algebras.- Ranges of spectral measures and Boolean algebras of projections.- Integral representation of the strongly closed algebra generated by a Boolean algebra of projections.- Bade functionals: an application to scalar-type spectral operators.- The reflexivity theorem and bicommutant algebras.- Bibliography.- Appendix.- List of symbols.- Subject index.

Product Details

ISBN:
9783540664611
Author:
Ricker, Werner
Publisher:
Springer
Location:
Berlin, Heidelberg
Subject:
General
Subject:
Algebra - Linear
Subject:
Algebra - Boolean
Subject:
Operator algebras
Subject:
Vector valued functions.
Subject:
Mathematical Analysis
Subject:
Projections
Subject:
spectral measures
Subject:
Operator theory
Subject:
Mathematics-Linear Algebra
Subject:
Functional Analysis
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
Book
Series:
Lecture Notes in Mathematics,
Series Volume:
1711
Publication Date:
19991029
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
176
Dimensions:
235 x 155 mm 590 gr

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Lecture Notes in Mathematics, #1711: Operator Algebras Generated by Commuting Projections: A Vector Measure Approach New Trade Paper
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