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Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

  • Book
  • © 1999

Overview

Authors:
  1. Werner Ricker
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1711)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Vector measures and Banach spaces

    • Werner Ricker
    Pages 1-24

  3. Abstract Boolean algebras and Stone spaces

    • Werner Ricker
    Pages 25-40

  4. Boolean algebras of projections and uniformly closed operator algebras

    • Werner Ricker
    Pages 41-56

  5. Ranges of spectral measures and Boolean algebras of projections

    • Werner Ricker
    Pages 57-66

  6. Integral representation of the strongly closed algebra generated by a Boolean algebra of projections

    • Werner Ricker
    Pages 67-90

  7. Bade functionals: an application to scalar-type spectral operators

    • Werner Ricker
    Pages 91-104

  8. The reflexivity theorem and bicommutant algebras

    • Werner Ricker
    Pages 105-119

  9. Back Matter

    Pages 121-160
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

  • Authors: Werner Ricker

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096184

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-66461-1Published: 17 September 1999

  • eBook ISBN: 978-3-540-48279-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 166

  • Topics: Operator Theory

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