Weak expectations and the injective envelope

Author:
Vern I. Paulsen

Journal:
Trans. Amer. Math. Soc. **363** (2011), 4735-4755

MSC (2010):
Primary 46L07; Secondary 47L25

DOI:
https://doi.org/10.1090/S0002-9947-2011-05203-7

Published electronically:
April 8, 2011

MathSciNet review:
2806689

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a unital -subalgebra we study the set of all possible images of the injective envelope of that are contained in and their position relative to the double commutant of the algebra in order to develop more information about the existence or non-existence of weak expectations. We study the set of all elements of that are fixed by all completely positive maps that fix We also introduce a new category, such that the injective envelope of in the new category is always contained in the double commutant of We study the relationship between these two injective envelopes and the existence of weak expectations.

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Additional Information

**Vern I. Paulsen**

Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476

Email:
vern@math.uh.edu

DOI:
https://doi.org/10.1090/S0002-9947-2011-05203-7

Keywords:
Weak expectation,
injective

Received by editor(s):
July 24, 2008

Received by editor(s) in revised form:
August 25, 2009, and September 1, 2009

Published electronically:
April 8, 2011

Additional Notes:
This research was supported in part by NSF grant DMS-0600191

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.