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arXiv · 2101.03751

Sur le spectre des op\'erateurs rigides

Pierre Mazet·Eric Saias
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Abstract

A bounded operator $u$ on $X$ is called rigid when there is an increasing sequence of positive integers $(n_k)_{k\geq 1}$, such that for every $x$ in $X$ we have $\lim_{k \rightarrow +\infty} u^{n_k} x = x$. For any $r$ in $[0,1]$, we construct a rigid bounded operator of $l^2$ the spectrum of which is $\{\lambda \in \mathbb C: r \leq | \lambda | \leq 1\}$. For $0 < r < 1$, it gives the first examples of rigid bounded invertible operators, such that their inverse is not rigid.

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Pierre Mazet, Eric Saias. 2021-01-11. Sur le spectre des op\'erateurs rigides. https://arxiv.org/abs/2101.03751

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