On the bicommutant for one type of J-symmetric nilpotent algebras in Krein spaces

In the present paper we shall consider an operator algebra in a Krein space. One of the interesting questions that arises in this area is a relationship between the algebra and its bicommutant. Here the question will be investigated for a J-symmetric weakly closed algebra that is nilpotent up to the...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 372; pp. 167 - 180
Main Author: Strauss, Vladimir
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.10.2003
Elsevier Science
Subjects:
Algebra
Bicommutant
Commutant
Exact sciences and technology
Indefinite metric
Linear and multilinear algebra, matrix theory
Mathematics
Operator algebra
Sciences and techniques of general use
Indefinite metric
Commutant
46K05
Bicommutant
46C20
Operator algebra
47B50
16W10
ISSN:0024-3795, 1873-1856
Online Access:Get full text
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Summary:In the present paper we shall consider an operator algebra in a Krein space. One of the interesting questions that arises in this area is a relationship between the algebra and its bicommutant. Here the question will be investigated for a J-symmetric weakly closed algebra that is nilpotent up to the identity operator and has an invariant subspace of a special type.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(03)00502-0