# Representations of the direct product of matrix algebras

Fundamenta Mathematicae (2001)

- Volume: 169, Issue: 2, page 145-160
- ISSN: 0016-2736

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topDaniele 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 -

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