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Some spectral inequalities involving generalized scalar operators

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Aupetit B., Drissi D.

Studia Mathematica

1994

tom 109

nr 1

51-66

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.

Ograniczanie wyników

1 Studia Mathematica

1 Aupetit B.

1 Drissi D.

1 1994

Wyniki wyszukiwania

Some spectral inequalities involving generalized scalar operators