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On the rate of change of spectra of operators

โœ Scribed by Rajendra Bhatia; Kalyan K. Mukherjea


Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
550 KB
Volume
27
Category
Article
ISSN
0024-3795

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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