Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

1. Auflage 1999
ISBN: 978-3-540-66461-1
Verlag: Springer

Buch, Englisch, Band 1711, 166 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 590 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Ricker, Werner

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.