The Spectral Mapping Theorem
Spectral Theory
2012-07-16 v4 Functional Analysis
Abstract
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.
Cite
@article{arxiv.1001.0232,
title = {The Spectral Mapping Theorem},
author = {Narinder S Claire},
journal= {arXiv preprint arXiv:1001.0232},
year = {2012}
}
Comments
latex 16 pages and 1 figure