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Multiplicative Spectra of Banach Spaces

✍ Scribed by S. A. Shkarin; Yu. N. Kuznetsova


Book ID
106433941
Publisher
Springer US
Year
2005
Tongue
English
Weight
162 KB
Volume
131
Category
Article
ISSN
1573-8795

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Let \(A \in \mathscr{L}(E)\) be a contraction. The famous Katznelson-Tzafriri theorem [11. Theorem 1] states that the spectral condition \(\sigma(A) \cap \Gamma \subseteq\{1\}\) is equivalent to the convergence of the orbit \(\left\{A^{n}(A-I): n=1,2, \ldots\right\}\) in norm to zero. Assume that th