Geodesic
Some spectral inequalities involving generalized scalar operators
Studia Mathematica, Tome 109 (1994) no. 1, pp. 51-66 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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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B. Aupetit. Some spectral inequalities involving generalized scalar operators. Studia Mathematica, Tome 109 (1994) no. 1, pp. 51-66. doi: 10.4064/sm-109-1-51-66

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