Weak Expectations and the Injective Envelope

Details Weak Expectations and the Injective Envelope Weak Expectations and the Injective Envelope

2008-07-18

arxiv.org/abs/0807.2982v1

Mathematics

Operator Algebras

Scientific paper

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.

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