Suppose B is a unital algebra which is an 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 2.6). 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 3.3).

Guido, D., & Tuset, L. (2001). Representations of the direct product of matrix algebras. FUNDAMENTA MATHEMATICAE, 169(2), 145-160.

### Representations of the direct product of matrix algebras

#### Abstract

Suppose B is a unital algebra which is an 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 2.6). 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 3.3).
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Settore MAT/05 - Analisi Matematica
eng
Con Impact Factor ISI
Banach algebras; irreducible representation; $\sigma$-complete ultrafilter
http://journals.impan.gov.pl/fm/Inf/169-2-4.html
Guido, D., & Tuset, L. (2001). Representations of the direct product of matrix algebras. FUNDAMENTA MATHEMATICAE, 169(2), 145-160.
Guido, D; Tuset, L
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/43710
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