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arXiv · 2002.06934

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

Christophe Cuny
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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 Ces\`aro 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.

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Christophe Cuny. 2020-02-17. Resolvent conditions and growth of powers of operators on $L^p$ spaces. https://arxiv.org/abs/2002.06934

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