Power regular operators

Atzmon, Aharon

doi:10.1090/S0002-9947-1995-1264802-7

Power regular operators
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by Aharon Atzmon

Trans. Amer. Math. Soc. 347 (1995), 3101-3109

DOI: https://doi.org/10.1090/S0002-9947-1995-1264802-7

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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 $\left \{ {{{\left \| {{T^n}x} \right \|}^{1/n}}} \right \}_{n = 1}^\infty$ 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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