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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Article copyright: © Copyright 1995 American Mathematical Society