Essential Spectrum and Feller Type Properties

We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy a new Feller type property, which we call 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,...

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Bibliographic Details
Published in:Integral equations and operator theory 2023-06, Vol.95 (2), Article 12
Main Authors: BenAmor, Ali, Güneysu, Batu, Stollmann, Peter
Format: Article
Language:English
Subjects:
Analysis
Dirichlet problem
Mathematics
Mathematics and Statistics
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Summary:We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy a new Feller type property, which we call 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 RCD ∗ spaces.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-023-02732-9