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arXiv · 2410.20725

Smooth Functional Calculus and Spectral Theorem in Banach Spaces

Luis A. Cedeño-Pérez·Hernando Quevedo
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Abstract

The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spectral Theorem to Banach algebras and operators between Banach spaces. To this end, we first develop a Smooth Functional Calculus in Banach algebras using the Cauchy-Pompeiu formula, which is further extended to a Continuous Functional Calculus. We also show that these theorems are proper generalizations of the usual result for operators between Hilbert spaces.

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BibTeXRIS

Luis A. Cedeño-Pérez, Hernando Quevedo. 2024-10-28. Smooth Functional Calculus and Spectral Theorem in Banach Spaces. https://arxiv.org/abs/2410.20725

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