# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Representations of the direct product of matrix algebras

### Tom 169 / 2001

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
Dipartimento di Matematica
Università della Basilicata
I-85100 Potenza, Italy
e-mail
• Lars TusetDipartimento di Matematica
Università di Roma “Tor Vergata”
I-00133 Roma, Italy
Faculty of Engineering
Oslo University College
0254 Oslo, Norway
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek