Some Directed Subsets of C*algebras and Semicontinuity Theory
Author:
Lawrence G. Brown
Journal:
Proc. Amer. Math. Soc. 143 (2015), 38953899
MSC (2010):
Primary 46L05
Published electronically:
May 1, 2015
MathSciNet review:
3359580
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Abstract: The main result concerns a unital algebra , a strongly lower semicontinuous element of , the enveloping von Neumann algebra, and the set of selfadjoint elements of such that for some , where 1 is the identity of . The theorem is that this set is directed upward. It follows that if this set is nonempty, then is the limit of an increasing net of selfadjoint elements of . A complement to the main result, which may be new even if , is that if and are selfadjoint in , , and for , then there is a selfadjoint in such that , and .
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 Gert K. Pedersen, algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], LondonNew York, 1979. MR 548006 (81e:46037)
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Additional Information
Lawrence G. Brown
Affiliation:
(Emeritus) Department of Mathematics, Purdue University, West Lafayette, Indiana 479072067
Email:
lgb@math.purdue.edu
DOI:
https://doi.org/10.1090/proc12744
Received by editor(s):
May 6, 2014
Published electronically:
May 1, 2015
Communicated by:
Marius Junge
Article copyright:
© Copyright 2015
American Mathematical Society
