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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