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Abstract. In this article we study bounded operators $T$ on a Banach space $X$ which satisfy the discrete Gomilko--Shi-Feng condition $\int _{0}^{2\pi }|\langle R(re^{it},T)^{2}x,x^*\rangle |dt \leq \frac {C}{(r^2-1)}\norme {x}\norme {x^*},\quad r>1, x\in X, x^* \in X^*$.
DOI: 10.14232/actasm-020-040-y
AMS Subject Classification
(1991): 47A60, 46B28, 42B35
Keyword(s):
$\gamma $-boundedness,
power bounded operators,
functional calculus,
Besov spaces
received 9.10.2020, revised 26.11.2020, accepted 6.12.2020. (Registered under 40/2020.)
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