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arXiv · 2204.09390

Essential spectrum and Feller type properties

Ali BenAmor·Batu Gueneysu·Peter Stollmann
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Abstract

We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy a new Feller type property, which we call \emph{weak Feller property}. Our characterization involves potential theoretic as well as probabilistic aspects and seems to be new even in the symmetric case. As a consequence, in the symmetric case, we obtain a new variant of a decomposition principle of the essential spectrum for (the self-adjoint operators induced by) regular symmetric Dirichlet forms and a Persson type theorem, which applies e.g. to Cheeger forms on $\mathsf{RCD^*}$ spaces.

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Ali BenAmor, Batu Gueneysu, Peter Stollmann. 2022-04-20. Essential spectrum and Feller type properties. https://arxiv.org/abs/2204.09390

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