Results 101 to 110 of about 99,725 (136)

Compact perturbations of scalar type spectral operators

Journal of Operator Theory, 2021
We consider compact perturbations S=DΛ+K of normal diagonal operators DΛ by certain compact operators. Sufficient conditions for K to ensure the existence of non-trivial hyperinvariant subspaces for S have recently been obtained by Foia\c{s} et al. in C.\ Foia\c{s}, I.B.\ Jung, E.\ Ko, C. Pearcy, \textit{J.\ Funct.
Albrecht, Ernst, Chevreau, Bernard
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Uniform operator σ-additivity of indefinite integrals induced by scalar-type spectral operators

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1985
SynopsisThis note characterises those Banach space valued, scalar-type spectral operators T = ∫ z dP(z), where P is the resolution of the identity for T, whose indefinite spectral integral E→∫EzdP(z) as a set function of the Borel sets of the complex plane is countably additive with respect to the uniform operator topology.
Okada, S., Ricker, W.
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On scalar-type spectral operators

Mathematical Proceedings of the Cambridge Philosophical Society, 1971
The purpose of this paper is to give two characterizations of scalar-type spectral operators.
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Scalar-type spectral operators andC(?)-operational calculi

Integral Equations and Operator Theory, 1990
It is shown that a continuous linear operatorT in a locally convex spaceX is a scalar-type spectral operator if and only if it admits aC(δ(T))-operational calculus of a certain kind. This is a genuine extension of previous results of this type since we allow for the case when δ(T){∞} is an unbounded set in the complex planeC, a phenomenon which occurs ...
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Spectra of Scalar‐Type Spectral Operators and Schauder Decompositions

Mathematische Nachrichten, 1988
Let H be a Hilbert space. It is well known that for any non-empty closed subset A of the complex plane there exists a normal operator T on H such that spectrum (T)\(=A\). In this paper the author shows that for an arbitrary Banach space X and A as above there may not exist a scalar type spectral operator [for definitions see \textit{N.
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