ACTA issues

## Derivative bounded functional calculus of power bounded operators on Banach spaces

Loris Arnold

Acta Sci. Math. (Szeged) 87:1-2(2021), 251-280
40/2020

 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.)