Thick Elements and States in -Algebras in View of Frame Theory

We study some classes of noncommutative -algebras and generalize some results which were originally obtained for commutative algebras in topological terms. In particular, we are interested in results obtained for topological spaces with properties close to separability and -compactness. To obtain th...

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Bibliographic Details
Published in:Russian journal of mathematical physics 2023, Vol.30 (2), p.184-191
Main Author: Fufaev, D. V.
Format: Article
Language:English
Subjects:
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639/766/189
639/766/530
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Algebra
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Topology
Online Access:Get full text
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Summary:We study some classes of noncommutative -algebras and generalize some results which were originally obtained for commutative algebras in topological terms. In particular, we are interested in results obtained for topological spaces with properties close to separability and -compactness. To obtain the algebraic, noncommutative versions of corresponding properties, we define and use the notions of thick elements and states. In particular, an element is thick if the only element orthogonal to it is zero.
ISSN:1061-9208
1555-6638
DOI:10.1134/S106192082302005X