3 papers
math.FA2020
Derivative bounded functional calculus of power bounded operators on Banach spaces
Loris Arnold
In this article we study bounded operators on Banach space which satisfy the discrete Gomilko Shi-Feng condition $$\int_{0}^{2π}|\langle R(re^{it},T)^{2}x,x^*\rangle |dt \l…
math.FA2019
Gamma-boundedness of -semigroups and their -functional calculi
Loris Arnold
We discuss the notion of --bounded calculus, strong ---bounded calculus on half-plane and weak--Gomilko-Shi-Feng condition and give a connection…
math.FA2018
New counterexamples on Ritt operators, sectorial operators and R-boundedness
Loris Arnold, Christian Le Merdy
Let be a Schauder decomposition on some Banach space . We prove that if is not -Schauder, then there exists a Ritt operator which is a m…