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1.
Dimosthenis Drivaliaris Sotirios Karanasios 《Linear algebra and its applications》2008,429(7):1555-1567
In this paper we characterize EP operators through the existence of different types of factorizations. Our results extend to EP operators existing characterizations for EP matrices and give new characterizations both for EP matrices and EP operators. 相似文献
2.
Lech Maligranda 《Acta Appl Math》1992,27(1-2):79-89
The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples. 相似文献
3.
Zen Harper 《Journal of Evolution Equations》2005,5(3):387-405
We study convolution operators on weighted Lebesgue spaces and obtain weight characterisations for boundedness of these operators
with certain kernels. Our main result is Theorem 3 which enables us to obtain results for certain kernel functions supported
on bounded intervals; in particular we get a direct proof of the known characterisations for Steklov operators in Section
3 by using the weighted Hardy inequality. Our methods also enable us to obtain new results for other kernel functions in Section
4. In Section 5 we demonstrate that these convolution operators are related to operators arising from the Weiss Conjecture
(for scalar-valued observation functionals) in linear systems theory, so that results on convolution operators provide elementary examples of nearly bounded semigroups
not satisfying the Weiss Conjecture. Also we apply results on the Weiss Conjecture for contraction semigroups to obtain boundedness
results for certain convolution operators. 相似文献
4.
Jean-Pierre Magnot 《Bulletin des Sciences Mathématiques》2008,132(2):112-127
In this article, we describe a class of algebras with unbounded operators on which the Schwinger cocycle extends. For this, we replace a space of bounded operators commonly used in the literature by some space of (maybe unbounded) tame operators, in particular by spaces of pseudo-differential operators, acting on the space of sections of a vector bundle E→M. We study some particular examples which we hope interesting or instructive. The case of classical and log-polyhomogeneous pseudo-differential operators is studied, because it carries other cocycles, defined with renormalized traces of pseudo-differential operators, that are some generalizations of the Khesin-Kravchenko-Radul cocycle. The present construction furnishes a simple proof of an expected result: The cohomology class of these cocycles are the same as cohomology class of the Schwinger cocycle. When M=S1, we show that the Schwinger cocycle is non-trivial on many algebras of pseudo-differential operators (these operators need not to be classical or bounded). These two results complete the work and extend the results of a previous work [J.-P. Magnot, Renormalized traces and cocycles on the algebra of S1-pseudo-differential operators, Lett. Math. Phys. 75 (2) (2006) 111-127]. When dim(M)>1, we furnish a new example of sign operator which could suggest that the framework of pseudo-differential operators is not adapted to all the cases. On this example, we have to work on some algebras of tame operators, in order to show that the Schwinger cocycle has a non-vanishing cohomology class. 相似文献
5.
A new iterative method for approximating fixed points of bounded and continuous pseudocontractive mapping is proposed and a strong convergence theorem is obtained. As an application, we prove that a slight modification of our new scheme could be employed for approximating zeros of bounded and continuous accretive operators. Our theorems extend and unify most of the results that have been proved for this class of mappings. 相似文献
6.
The gap between hyponormal and subnormal Hilbert space operators can be studied using the intermediate classes of weakly n-hyponormal and (strongly) n-hyponormal operators. The main examples for these various classes, particularly to distinguish them, have been the weighted
shifts. In this paper we first obtain a characterization for a weakly n-hyponormal weighted shift Wα with weight sequence α, from which we extend some known results for quadratically hyponormal (i.e., weakly 2-hyponormal)
weighted shifts to weakly n-hyponormal weighted shifts. In addition, we discuss some new examples for weakly n-hyponormal weighted shifts; one illustrates the differences among the classes of 2-hyponormal, quadratically hyponormal,
and positively quadratically hyponormal operators. 相似文献
7.
Perturbation determinants in Banach spaces — with an application to eigenvalue estimates for perturbed operators 下载免费PDF全文
Marcel Hansmann 《Mathematische Nachrichten》2016,289(13):1606-1625
In the first part of this paper we provide a self‐contained introduction to (regularized) perturbation determinants for operators in Banach spaces. In the second part, we use these determinants to derive new bounds on the discrete eigenvalues of compactly perturbed operators, broadly extending some recent results by Demuth et al. In addition, we also establish new bounds on the discrete eigenvalues of generators of C0‐semigroups. 相似文献
8.
Victoria Martín-Márquez Simeon Reich Shoham Sabach 《Nonlinear Analysis: Theory, Methods & Applications》2012
We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize sunny right quasi-Bregman nonexpansive retractions, and as a consequence, we show that the fixed point set of any right quasi-Bregman nonexpansive operator is a sunny right quasi-Bregman nonexpansive retract of the ambient Banach space. 相似文献
9.
On a class of quasi-Fredholm operators 总被引:1,自引:0,他引:1
M. Berkani 《Integral Equations and Operator Theory》1999,34(2):244-249
We study a class of bounded linear operators acting on a Banach spaceX called B-Fredholm operators. Among other things we characterize a B-Fredholm operator as the direct sum of a nilpotent operator and a Fredholm operator and we prove a spectral mapping theorem for B-Fredholm operators.IMemory of my father, Sidi-Bouhouria 1914-0991. 相似文献
10.
Bamdad R. Yahaghi 《Linear algebra and its applications》2008,428(4):1151-1168
In this paper we consider collections of compact (resp. Cp class) operators on arbitrary Banach (resp. Hilbert) spaces. For a subring R of reals, it is proved that an R-algebra of compact operators with spectra in R on an arbitrary Banach space is triangularizable if and only if every member of the algebra is triangularizable. It is proved that every triangularizability result on certain collections, e.g., semigroups, of compact operators on a complex Banach (resp. Hilbert) space gives rise to its counterpart on a real Banach (resp. Hilbert) space. We use our main results to present new proofs as well as extensions of certain classical theorems (e.g., those due to Kolchin, McCoy, and others) on arbitrary Banach (resp. Hilbert) spaces. 相似文献
11.
Nathan S. Feldman 《Integral Equations and Operator Theory》2000,37(4):402-422
We study pure subnormal operators whose self-commutators have zero as an eigenvalue. We show that various questions in this are closely related to questions involving approximation by functions satisfying
and to the study ofgeneralized quadrature domains.First some general results are given that apply to all subnormal operators within this class; then we consider characterizing the analytic Toeplitz operators, the Hardy operators and cyclic subnormal operators whose self-commutators have zero as an eigenvalue. 相似文献
12.
Zen Harper 《Integral Equations and Operator Theory》2006,54(1):69-88
In this paper, we study a discrete version of the Weiss Conjecture. In Section 1 we discuss the Reproducing Kernel Thesis
and in Section 2 we introduce the operators which concern us. Section 3 shows how to relate these operators to Carleson embeddings
and weighted composition operators, so that we can apply the Carleson measure theorem to obtain conditions for boundedness
and compactness of many weighted composition operators. Section 4 contains Theorem 4.4 which is a discrete version of the
Weiss Conjecture for contraction semigroups, and finally Section 5 shows how the usual (continuous time) Weiss Conjecture
is related to the discrete version studied here; in fact they are equivalent (for scalar valued observation operators). The
main advantage of the discrete version is that it is technically simpler – the observation operators are automatically bounded
and the functional calculus can be achieved using power series. 相似文献
13.
In this paper we define an equivalence relation of operators on Hilbert spaces which we call absolute equivalence. Two operators are called absolutely equivalent if both the absolute value of the operators and their adjoints are unitarily equivalent. We then use the properties of this equivalence relation to study the Koszul complex of a commuting tuple of operators through the Dirac operator of the tuple. 相似文献
14.
Generalized Anti-Wick operators are introduced as a class of
pseudodifferential operators which depend on a symbol and two different window
functions. Using symbols in Sobolev spaces with negative smoothness and
windows in so-called modulation spaces, we derive new conditions for the
boundedness on L2 of such operators and for their membership in the Schatten
classes. These results extend and refine results contained in [20], [10], [5],
[4], and [14]. 相似文献
15.
M. I. Gil’ 《Integral Equations and Operator Theory》2006,54(3):317-331
A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued
functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the
obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the mentioned results
to integro-differential equations are also discussed. 相似文献
16.
Hideaki Iiduka Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3679-3688
In this paper, we study a strong convergence for monotone operators. We first introduce the hybrid type algorithm for monotone operators. Next, we obtain a strong convergence theorem (Theorem 3.3) for finding a zero point of an inverse-strongly monotone operator in a Banach space. Finally, we apply our convergence theorem to the problem of finding a minimizer of a convex function. 相似文献
17.
In this paper, we obtain an existence theorem for single-valued monotone operators in a reflexive Banach space. Using this
result, we prove a fixed point theorem for nonexpansive mappings in a Hilbert space and an existence theorem for maximal monotone
operators in a Banach space.
Received: 3 July 2006 Revised: 15 January 2007 相似文献
18.
Amro Alsheikh Ali 《Quaestiones Mathematicae》2016,39(3):319-340
In this paper, we establish some new nonlinear Leray-Schauder alternatives for the sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. As an application, our results are used to prove the existence of solutions for a nonlinear integral equation. 相似文献
19.
B. Nagy 《Periodica Mathematica Hungarica》1980,11(1):1-6
The various essential spectra of a linear operator have been surveyed byB. Gramsch andD. Lay [4]. In this paper we characterize the essential spectra and the related quantities nullity, defect, ascent and descent of bounded spectral operators. It is shown that a number of these spectra coincide in the case of a spectral or a scalar type operator. Some results known for normal operators in Hilbert space are extended to spectral operators in Banach space. 相似文献
20.
Matthew Kennedy Victor S. Shulman Yuri V. Turovskii 《Integral Equations and Operator Theory》2009,63(1):47-93
We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence
are imposed on certain components of the subgrading. This allows us to obtain some useful information about the structure
of such algebras. As an application, we prove a number of results on the existence of invariant subspaces for algebraic structures
of compact operators, in particular for Jordan algebras and Lie triple systems of Volterra operators. Along the way we obtain
new criteria for the triangularizability of a Lie algebra of compact operators.
The support received from INTAS project No 06-1000017-8609 is gratefully acknowledged by the third author. 相似文献