Weak expectations and the injective envelope
Author:
Vern I. Paulsen
Journal:
Trans. Amer. Math. Soc. 363 (2011), 47354755
MSC (2010):
Primary 46L07; Secondary 47L25
Published electronically:
April 8, 2011
MathSciNet review:
2806689
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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 nonexistence 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 772043476
Email:
vern@math.uh.edu
DOI:
http://dx.doi.org/10.1090/S000299472011052037
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 DMS0600191
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
