Copy For Citation
Mustafayev H.
INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.92, no.4, 2020 (SCI-Expanded)
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Publication Type:
Article / Article
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Volume:
92
Issue:
4
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Publication Date:
2020
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Doi Number:
10.1007/s00020-020-02591-8
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Journal Name:
INTEGRAL EQUATIONS AND OPERATOR THEORY
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Journal Indexes:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
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Keywords:
Hilbert space, Banach space, Compact operator, Toeplitz operator, Composition operator, Model operator, Local spectrum, Operator sequence, Operator average, Convergence
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Van Yüzüncü Yıl University Affiliated:
Yes
Abstract
Let A, T, and B be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences {A(n)TB(n)} and {1/n Sigma(n-1)(i=0) A(i)TB(i)}. These results are applied to the Toeplitz, composition, and model operators. Some related problems are also discussed.