Displaying similar documents to “On the bounded cosine operator function in Banach space”

Perturbation theorems for Hermitian elements in Banach algebras

Rajendra Bhatia, Driss Drissi (1999)

Studia Mathematica

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Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.

Some spectral inequalities involving generalized scalar operators

B. Aupetit, D. Drissi (1994)

Studia Mathematica

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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,...