Results 191 to 200 of about 2,144 (211)

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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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
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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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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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Spectral Operators of Scalar Type in Grothendieck Spaces with the Dunford-Pettis Property

Bulletin of the London Mathematical Society, 1985
It is shown that if S is a continuous linear operator in a Banach space which is a Grothendieck space with the Dunford-Pettis property, then \(S=\sum^{m}_{j=1}z_ jP_ j\) for some complex numbers \(z_ j\) and disjoint commuting projections \(P_ j\), \(1\leq j\leq m\), whose sum is the identity operator. The proof is based on the fact that in such Banach
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Well-Bounded and Scalar-Type Spectral Operators on L^p Spaces

Journal of the London Mathematical Society, 1989
A well-bounded operator on a Banach space X is one which admits a functional calculus for the absolutely continuous functions on some compact interval of the real line. On Hilbert space it is known that every well-bounded operator with a contactive absolutely continuous functional calculus is self-adjoint.
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On Reflexive Scalar-Type Spectral Operators

Journal of the London Mathematical Society, 1974
Berkson, E., Dowson, H. R.
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On scalar-type spectral operators and Carleman ultradifferentiable C???-semigroups

2020
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Restrictions of Scalar-Type Spectral Operators

Bulletin of the London Mathematical Society, 1978
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When is a non-self-adjoint Hill operator a spectral operator of scalar type?

Comptes Rendus Mathematique, 2006
Fritz Gesztesy
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