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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Power regular operators


Author: Aharon Atzmon
Journal: Trans. Amer. Math. Soc. 347 (1995), 3101-3109
MSC: Primary 47A10; Secondary 47B40
MathSciNet review: 1264802
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Abstract: We show that for a wide class of operators $ T$ on a Banach space, including the class of decomposable operators, the sequence $ \left\{ {{{\left\Vert {{T^n}x} \right\Vert}^{1/n}}} \right\}_{n = 1}^\infty $ converges for every $ x$ in the space to the spectral radius of the restriction of $ T$ to the subspace $ \vee _{n = 0}^\infty \{ {T^n}x\} $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1264802-7
PII: S 0002-9947(1995)1264802-7
Article copyright: © Copyright 1995 American Mathematical Society