Representations of the direct product of matrix algebras

Tom 169 / 2001

Daniele Guido, Lars Tuset Fundamenta Mathematicae 169 (2001), 145-160 MSC: Primary 46-XX; Secondary 03E55. DOI: 10.4064/fm169-2-4

Streszczenie

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).

Autorzy

  • Daniele GuidoDipartimento 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
    e-mail
  • Lars TusetDipartimento 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
    e-mail

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