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Title

Some spectral inequalities involving generalized scalar operators

Authors 1, 1

Affiliations

  1. Département de Mathématiques et de Statistique, Université Laval, Québec, Qué., Canada G1K 7P4

Abstract

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.

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Studia Mathematica
1994/109/1
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Pages:
51-66
Main language of publication
English
Received
1993-01-07
Accepted
1993-06-09
Published
1994
Exact and natural sciences