Representations of the direct product of matrix algebras

Daniele Guido, and Lars Tuset. "Representations of the direct product of matrix algebras." Fundamenta Mathematicae 169.2 (2001): 145-160. <http://eudml.org/doc/282363>.

@article{DanieleGuido2001,
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 σ-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).},
author = {Daniele Guido, Lars Tuset},
journal = {Fundamenta Mathematicae},
keywords = {Banach algebras; irreducible representation; -complete ultrafilter},
language = {eng},
number = {2},
pages = {145-160},
title = {Representations of the direct product of matrix algebras},
url = {http://eudml.org/doc/282363},
volume = {169},
year = {2001},
}

TY - JOUR
AU - Daniele Guido
AU - Lars Tuset
TI - Representations of the direct product of matrix algebras
JO - Fundamenta Mathematicae
PY - 2001
VL - 169
IS - 2
SP - 145
EP - 160
AB - 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 σ-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).
LA - eng
KW - Banach algebras; irreducible representation; -complete ultrafilter
UR - http://eudml.org/doc/282363
ER -