Results 211 to 220 of about 109,954 (249)

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.
S. Okada, W. Ricker
semanticscholar   +3 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.
S. Okada
semanticscholar   +2 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
semanticscholar   +3 more sources

Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result

Asymptotic Analysis, 2022
We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface ...
Maximilian Moser
semanticscholar   +1 more source

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.
openaire   +2 more sources

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 ...
openaire   +1 more source

Principal spectral curves for Lane–Emden fully nonlinear type systems and applications

Calculus of Variations and Partial Differential Equations, 2020
In this paper we exploit the phenomenon of two principal half eigenvalues in the context of fully nonlinear Lane–Emden type systems with possibly unbounded coefficients and weights.
Ederson Moreira dos Santos, Gabrielle Nornberg, Delia Schiera, H. Tavares   +3 more
semanticscholar   +1 more source

Schnol’s Theorem and Spectral Properties of Massless Dirac Operators with Scalar Potentials

Letters in Mathematical Physics, 2013
The spectra of massless Dirac operators are of essential interest, e.g., for the electronic properties of graphene, but fundamental questions such as the existence of spectral gaps remain open.
K. Schmidt, T. Umeda
semanticscholar   +1 more source

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
openaire   +2 more sources

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.
openaire   +1 more source