Results 201 to 210 of about 9,405,925 (227)

On Scalar-Type Spectral Operators

open access: yesMathematical Proceedings of the Cambridge Philosophical Society, 1971
The purpose of this paper is to give two characterizations of scalar-type spectral operators.
P G Spain
exaly   +4 more sources

Uniform operator σ-additivity of indefinite integrals induced by scalar-type spectral operators

open access: yesProceedings 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.
openaire   +3 more sources

A Spectral Mapping Theorem for Scalar-Type Spectral Operators in Locally Convex Spaces

Integral Equations and Operator Theory, 1985
Let T be a continuous scalar-type spectral operator defined on a quasicomplete locally convex space X, that is, \(T=\int fdP\) where P is an equicontinuous spectral measure in X and f is a P-integrable function. It is shown that \(\sigma\) (T) is precisely the closed P-essential range of the function f or, equivalently, that \(\sigma\) (T) is equal to ...
W Ricker
exaly   +3 more sources

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
openaire   +2 more sources

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.
openaire   +1 more source

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