Resolvent conditions and growth of powers of operators on $L^p$ spaces

Abstract

Let $T$ be a bounded linear operator on $L^p$. We study the rate of growth of the norms of the powers of $T$ under resolvent conditions or Cesàro boundedness assumptions. Actually the relevant properties of $L^p$ spaces in our study are their type and cotype, and for $1<p<\infty$, the fact that they are UMD. Some of the proofs make use of Fourier multipliers on Banach spaces, which explains why UMD spaces come into play.

14 pages

References in corpus (1)

• Kreiss bounded and uniformly Kreiss bounded operators

Cited by in corpus (1)

• Growth rate of eventually positive Kreiss bounded $C_0$-semigroups on $L^p$ and $\mathcal{C}(K)$