Results 11 to 20 of about 13,630 (223)
Scalar-type spectral operators and holomorphic semigroups
Semigroup Forum, 1986 We show that a linear operator (possibly unbounded), A, on a reflexive Banach space, X, is a scalar-type spectral operator, with non-negative spectrum, if and only if the following conditions hold. (1) A generates a uniformly bounded holomorphic semigroup \(\{e^{- zA}\}_{Re(z)\geq 0}.\) (2) If \(F_ N(s)\equiv \int^{N}_{-N}\frac{\sin (sr)}{r}e^{irA}dr\),
R. Laubenfels
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On the characterization of scalar type spectral operators [PDF]
Studia Mathematica, 2008 The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.
P. A. Cojuhari, A. M. Gomilko
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When is a non-self-adjoint Hill operator a spectral operator of scalar type? [PDF]
Comptes Rendus. Mathématique, 2005 5 ...
Gesztesy, Fritz, Tkachenko, Vadim
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Algebras of unbounded scalar-type spectral operators [PDF]
Pacific Journal of Mathematics, 1987 The main result of the paper is as follows. Let P:\(\Sigma\to L(X)\) be a closed spectral measure on the quasicomplete locally convex space X and T a densely defined linear operator on X with domain invariant under each operator of the form \(\int_{\Omega}fdP\), where f is a complex bounded \(\Sigma\)-measurable function.
Dodds, P.G. (author) +1 more
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On Boolean algebras of projections and scalar-type spectral operators [PDF]
Proceedings of the American Mathematical Society, 1983 It is shown that the weakly closed operator algebra generated by an equicontinuous σ \sigma
W. Ricker
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Reflexivity and order properties of scalar-type spectral operators in locally convex spaces [PDF]
Transactions of the American Mathematical Society, 1986 One of the principal results of the paper is that each scalar-type spectral operator in the quasicomplete locally convex space X X
Dodds, P. G., de Pagter, B., Ricker, W.
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ON REFLEXIVITY OF SCALAR-TYPE SPECTRAL OPERATORS
Demonstratio Mathematica, 1999 \(X\) is said to be a locally convex \(C(K)\)-module if the bilinear mapping \(C(K)\times X\to X:(a, x)\to ax\) satisfies the following conditions: (i) 1. \(x= x\) for all \(x\) in \(X\), (ii) \((a,b)x= a.(bx)\) \((a\in C(K),b\in C(K),x\in X)\), (iii) the bilinear mapping is separately continuous. Here \(K\) is a compact Hausdorff space.
Omer Goek
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Boolean algebras of projections and resolutions of the identity of scalar-type spectral operators [PDF]
Proceedings of the Edinburgh Mathematical Society, 1997 Let Μ be a Bade complete (or σ-complete) Boolean algebra of projections in a Banach space X. This paper is concerned with the following questions: When is Μ equal to the resolution of the identity (or the strong operator closure of the resolution of the identity) of some scalar-type spectral operator T (with σ(T) ⊆ ℝ) in X?
De Pagter, B., Ricker, W. J.
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On the non-hypercyclicity of scalar type spectral operators and collections of their exponentials
Demonstratio Mathematica, 2020 Abstract Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a scalar type spectral operator A in a complex Banach space as well as of the collection
Marat V Markin
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On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable C0‐semigroups [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
M. V. Markin
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