Essential positivity

arxiv（2023）

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摘要

We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the non-negative real numbers and describe their basic properties. Using Toeplitz operators and the Berezin transform, we further illustrate the notion of essential positivity in the Hardy space and the Bergman space.

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关键词

Essential positivity,Berezin transform,Toeplitz operators,Bergman space

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