Title : ( Simple reduced Lp-operator crossed products with unique trace )
Authors: Shirin Hejazian , Sanaz Pooya ,
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Abstract
Given p>1, let G be a countable Powers group, and let (G, A, a) be a separable nondegenerately representable isometric G-Lp-operator algebra. We show that if A is unital and G-simple then the reduced Lp-operator crossed product of A by G is simple. Furthermore, traces on this crossed product are in natural bijection with G-invariant traces on A via the standard conditional expectation. In particular, if A has a unique normalized trace then so does Fp. These results generalize special cases of some results due to de la Harpe and Skanadalis in the case of C*-algebras.
Keywords
, Lp-operator algebra, G-Lp-operator algebra, covariant representation, regular covariant representation, crossed product, Powers group, G-invariant ideal, simple algebra, trace.
@article{paperid:1049404,
author = {Hejazian, Shirin and Pooya, Sanaz},
title = {Simple reduced Lp-operator crossed products with unique trace},
journal = {Journal of Operator Theory},
year = {2015},
volume = {74},
number = {1},
month = {July},
issn = {0379-4024},
pages = {133--147},
numpages = {14},
keywords = {Lp-operator algebra; G-Lp-operator algebra; covariant representation;
regular covariant representation; crossed product; Powers group; G-invariant ideal;
simple algebra; trace.},
}
%0 Journal Article
%T Simple reduced Lp-operator crossed products with unique trace
%A Hejazian, Shirin
%A Pooya, Sanaz
%J Journal of Operator Theory
%@ 0379-4024
%D 2015
