On Weak Decay Rates and Uniform Stability of Bounded Linear Operators

Jochen Glück

doi:10.1007/s00013-015-0746-5

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arXiv · 1501.05834

On Weak Decay Rates and Uniform Stability of Bounded Linear Operators

Jochen Glück

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Abstract

We consider a bounded linear operator $T$ on a complex Banach space $X$ and show that its spectral radius $r(T)$ satisfies $r(T) < 1$ if all sequences $(< x',T^nx>)_{n \in \mathbb{N}_0}$ ($x \in X$, $x' \in X'$) are, up to a certain rearrangement, contained in a principal ideal of the space $c_0$ of sequences which converge to $0$. From this result we obtain generalizations of theorems of G. Weiss and J. van Neerven. We also prove a related result on $C_0$-semigroups.

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BibTeX RIS

Jochen Glück. 2015-02-11. On Weak Decay Rates and Uniform Stability of Bounded Linear Operators. https://doi.org/10.1007/s00013-015-0746-5

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