Representations of Direct Product of Matrix Algebras
Operator Algebras
2007-05-23 v2 Logic
Abstract
Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the sigma-complete ultrafilters on X, Theorem 1. Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described, Theorem 3.
Keywords
Cite
@article{arxiv.math/9907006,
title = {Representations of Direct Product of Matrix Algebras},
author = {Daniele Guido and Lars Tuset},
journal= {arXiv preprint arXiv:math/9907006},
year = {2007}
}
Comments
18 pages, Latex. Minor modifications, one reference added, to appear on Fund. Math