Strongly Kreiss Bounded Operators in UMD Banach Spaces

Abstract

In this paper we give growth estimates for $\Vert T^n\Vert$ for $n\to \infty$ in the case $T$ is a strongly Kreiss bounded operator on a UMD Banach space $X$. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and $L^p$-spaces, but also intermediate UMD spaces such as non-commutative $L^p$-spaces and variable Lebesgue spaces.

arXiv comment27 pages, minor corrections

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• Banach function spaces done right
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