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On the possible values of the index of Noetherian operators in a pair of Banach spaces

✍ Scribed by I. Ya. Shneiberg


Publisher
Springer US
Year
1973
Tongue
English
Weight
150 KB
Volume
7
Category
Article
ISSN
0016-2663

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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