Limit operators techniques on general metric measure spaces of bounded geometry

Abstract

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit operators, characterizations of compactness and Fredholmness using limit operators; and thus also spectral consequences. In this way, we recover and unify the classical and recent results on limit operator techniques, but also gain new insights and are able to treat further applications.

References in corpus (6)

• Some notes on property A
• An Affirmative Answer to a Core Issue on Limit Operators
• Fredholm theory for band-dominated and related operators: a survey
• Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices
• Fredholmness of Toeplitz operators on the Fock space
• Fock-Sobolev spaces and their Carleson measures

Cited by in corpus (3)

• Fredholm Toeplitz operators on doubling Fock spaces
• Growth of Eigenfunctions and R-limits on Graphs
• C*-Algebraic Spectral Sets, Twisted Groupoids and Operators