The Spectral Mapping Theorem

Details The Spectral Mapping Theorem The Spectral Mapping Theorem

2010-01-03

arxiv.org/abs/1001.0232v4

Mathematics

Spectral Theory

latex 16 pages and 1 figure

Scientific paper

We give a direct non-abstract proof of the Spectral Mapping Theorem for the Helffer-Sj\"ostrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new non-abstract direct proof for the Spectral Mapping Theorem for self-adjoint operators on Hilbert spaces. Our exposition is closer in spirit to the proof by explicit construction of the existence of the Functional Calculus given by Davies. We apply an extension theorem of Seeley to derive a functional calculus for semi-bounded operators.

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