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arXiv · 2206.13955

Spectral mapping theorems for essential spectra and regularized functional calculi

Jesús Oliva-Maza
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Abstract

Gramsch and Lay [10] gave spectral mapping theorems for the Dunford-Taylor calculus of a closed linear operator $T$, $$\widetildeσ_i(f(T)) = f(\widetildeσ_i(T)), $$ for several extended essential spectra $\widetildeσ_i$. In this work, we extend such theorems for the natural functional calculus introduced by Haase [12,13]. We use the model case of bisectorial operators. The proofs presented here are generic, and are valid for similar functional calculus.

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Jesús Oliva-Maza. 2023-01-04. Spectral mapping theorems for essential spectra and regularized functional calculi. https://arxiv.org/abs/2206.13955

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