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921.
J.M. Calabuig E.A. Sánchez-Pérez 《Journal of Mathematical Analysis and Applications》2011,373(1):316-321
Let X be a Banach space and E an order continuous Banach function space over a finite measure μ. We prove that an operator T in the Köthe-Bochner space E(X) is a multiplication operator (by a function in L∞(μ)) if and only if the equality T(g〈f,x∗〉x)=g〈T(f),x∗〉x holds for every g∈L∞(μ), f∈E(X), x∈X and x∗∈X∗. 相似文献
922.
A version of Orlicz-Pettis Theorem is established for multiplier convergent series and quasi-homogeneous operator. Applications to spaces of quasi-homogeneous operators are given. 相似文献
923.
Caishi Wang Yanchun Lu Huifang Chai 《Journal of Mathematical Analysis and Applications》2011,373(2):643-654
In this paper, we present an alternative approach to Privault's discrete-time chaotic calculus. Let Z be an appropriate stochastic process indexed by N (the set of nonnegative integers) and l2(Γ) the space of square summable functions defined on Γ (the finite power set of N). First we introduce a stochastic integral operator J with respect to Z, which, unlike discrete multiple Wiener integral operators, acts on l2(Γ). And then we show how to define the gradient and divergence by means of the operator J and the combinatorial properties of l2(Γ). We also prove in our setting the main results of the discrete-time chaotic calculus like the Clark formula, the integration by parts formula, etc. Finally we show an application of the gradient and divergence operators to quantum probability. 相似文献
924.
This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoar? and Foias (1968) [1]. 相似文献
925.
Decio Levi Piergiulio Tempesta 《Journal of Mathematical Analysis and Applications》2011,376(1):247-258
We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled equations are of finite order. Our results are applied to the study of multiple-scale reductions of dynamical systems, and in particular to the case of a discrete nonlinear harmonic oscillator. 相似文献
926.
Jorge Cossio Sigifredo Herrón 《Journal of Mathematical Analysis and Applications》2011,376(2):741-749
We prove the existence of infinitely many radial solutions for a p-Laplacian Dirichlet problem which is p-superlinear at the origin. The main tool that we use is the shooting method. We extend for more general nonlinearities the results of J. Iaia in [J. Iaia, Radial solutions to a p-Laplacian Dirichlet problem, Appl. Anal. 58 (1995) 335-350]. Previous developments require a behavior of the nonlinearity at zero and infinity, while our main result only needs a condition of the nonlinearity at zero. 相似文献
927.
C.J. Read 《Journal of Mathematical Analysis and Applications》2011,381(1):202-217
We show that in every nonzero operator algebra with a contractive approximate identity (or c.a.i.), there is a nonzero operator T such that ‖I−T‖?1. In fact, there is a c.a.i. consisting of operators T with ‖I−2T‖?1. So, the numerical range of the elements of our contractive approximate identity is contained in the closed disk center and radius . This is the necessarily weakened form of the result for C?-algebras, where there is always a contractive approximate identity consisting of operators with 0?T?1 - the numerical range is contained in the real interval [0,1]. So, if an operator algebra has a c.a.i., it must have operators with a “certain amount” of positivity. 相似文献
928.
Zhongying Chen 《Journal of Mathematical Analysis and Applications》2011,383(2):522-1258
In this paper, we generalize the complex shifted Laplacian preconditioner to the complex shifted Laplacian-PML preconditioner for the Helmholtz equation with perfectly matched layer (Helmholtz-PML equation). The Helmholtz-PML equation is discretized by an optimal 9-point difference scheme, and the preconditioned linear system is solved by the Krylov subspace method, especially by the biconjugate gradient stabilized method (Bi-CGSTAB). The spectral analysis of the linear system is given, and a new matrix-based interpolation operator is proposed for the multigrid method, which is used to approximately invert the preconditioner. The numerical experiments are presented to illustrate the efficiency of the preconditioned Bi-CGSTAB method with the multigrid based on the new interpolation operator, also, numerical results are given for comparing the performance of the new interpolation operator with that of classic bilinear interpolation operator and the one suggested in Erlangga et al. (2006) [10]. 相似文献
929.
Thomas Ryan Harris Michael Mazzella David Renfrew Ilya M. Spitkovsky 《Linear algebra and its applications》2011,435(11):2639-2657
The numerical range of a bounded linear operator T on a Hilbert space H is defined to be the subset W(T)={〈Tv,v〉:v∈H,∥v∥=1} of the complex plane. For operators on a finite-dimensional Hilbert space, it is known that if W(T) is a circular disk then the center of the disk must be a multiple eigenvalue of T. In particular, if T has minimal polynomial z3-1, then W(T) cannot be a circular disk. In this paper we show that this is no longer the case when H is infinite dimensional. The collection of 3×3 matrices with three-fold symmetry about the origin are also classified. 相似文献
930.
We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ?. We study the structure of generators of the Banach algebras (C(n)[0, 1], *) and (C(n)[0, 1], ?). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space Lp[0, 1] by the formula (Cφf)(x) = f(φ(x)). 相似文献