Representations of the direct product of matrix algebras

Daniele Guido¹ ; Lars Tuset²

¹ Dipartimento di Matematica Università di Roma “Tor Vergata” I-00133 Roma, Italy Present address: Dipartimento di Matematica Università della Basilicata Contrada Macchia Romana I-85100 Potenza, Italy
² Dipartimento di Matematica Università di Roma “Tor Vergata” I-00133 Roma, Italy Present address: Faculty of Engineering Oslo University College Cort Adelers Gate 30 0254 Oslo, Norway

Fundamenta Mathematicae, Tome 169 (2001) no. 2, pp. 145-160.

Résumé

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).

Détail

DOI : 10.4064/fm169-2-4

Keywords: suppose unital algebra which algebraic product full matrix algebras index set bijection set between equivalence classes irreducible representations operators banach space sigma complete ultrafilters theorem therefore has measurable cardinality accessible equivalence classes irreducible representations labeled points representations described theorem