Operator Algebras Generated by Commuting Projections: A Vector Measure Approach

• Main Author: Ricker, Werner (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1711
• Subjects: Operator theory.; Operator Theory.

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 emp...

Table of Contents:

• 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.