Power Regular Operators
Aharon Atzmon · Transactions of the American Mathematical Society · 1995
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 $\vee _{n = 0}^\infty \{ {T^n}x\}$.