In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu, Barnes, Pytlik, Boyadzhiev and others.
@article{bwmeta1.element.bwnjournal-article-smv109i1p51bwm,
author = {B. Aupetit and D. Drissi},
title = {Some spectral inequalities involving generalized scalar operators},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {51-66},
zbl = {0829.47002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p51bwm}
}
Aupetit, B.; Drissi, D. Some spectral inequalities involving generalized scalar operators. Studia Mathematica, Tome 108 (1994) pp. 51-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p51bwm/
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