Weak Expectations and the Injective Envelope

2008/07/18 by Vern I. Paulsen, Paulsen, Vern I. · 3 citations
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.OA #msc:46L15

paper · pdf · doi:10.48550/arxiv.0807.2982

arxiv created 2008/07/18 · arxiv updated 2009/12/01

Abstract

Given a unital C*-subalgebra of B(H), we study the set of all possible images of its injective envelope that are contained in B(H) and their position relative to the double commutant of the algebra in order to obtain more information about the existence or non-existence of weak expectations. We study the subset of B(H) that is the intersection of all possible images of the injective envelope and show that it is simultaneously a reflexive cover and a new type of order completion of the algebra.

Cited by

• Ideals and structure of operator algebras
• A short proof of the existence of the injective envelope of an operator space
• The Hao-Ng isomorphism theorem for reduced crossed products

Related

• Characterisations of the weak expectation property
• Injective Envelopes of Separable C*-algebras
• The strong Morita equivalence for inclusions of C^*-algebras and conditional expectations for equivalence bimodules
• Injective envelopes for locally C*-algebras
• Unique conditional expectations for abelian C^*-inclusions