共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl-Titchmarsh matrix-valued functions as well as a new version of the functional model for such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-valued functions, we provide a complete characterization of their realizations in terms of the corresponding functional model. We also obtain properties of a symmetric operator and its self-adjoint extension which generate a periodic Weyl-Titchmarsh matrix-valued function. We study pairs of operators (a symmetric operator and its self-adjoint extension) with constant Weyl-Titchmarsh matrix-valued functions and establish connections between such pairs of operators and representations of the canonical commutation relations for unitary groups of operators in Weyl's form. As a consequence of such an approach, we obtain the Stone-von Neumann theorem for two unitary groups of operators satisfying the commutation relations as well as some extension and refinement of the classical functional model for generators of those groups. Our examples include multiplication operators in weighted spaces, first and second order differential operators, as well as the Schrödinger operator with linear potential and its perturbation by bounded periodic potential. 相似文献
2.
GAO Mingchu Department of Mathematics University of Illinois at Urbana-Champaign Urbana IL USA 《中国科学A辑(英文版)》2006,49(6):800-819
Certain free products are introduced for operator spaces and dual operator spaces. It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C*-algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C*-algebra-reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces. 相似文献
3.
This note concerns a class of Wiener-Hopf operators on a finite interval, acting between Sobolev multi-index spaces. Necessary and sufficient conditions for such an operator to be Fredholm are given, as well as a formula for the index. The argument is based on a reduction procedure of convolution operators on a finite interval to operators of the same type on the half-line.supported by the Netherlands organization for scientific research (NWO)supported in part by NSF Grant 9101143 相似文献
4.
Pedro A. Santos 《Mathematische Nachrichten》2001,232(1):95-127
The purpose of this paper is to obtain necessary and sufficient conditions for maximum defect spline approximation methods with uniform meshes to be stable. The methods are applied to operators belonging to the closed subalgebra of ℒ︁ (L2 (ℝ)) generated by operators of multiplication by piecewise continuous functions on ℝ and convolution operators also with piecewise continuousgenerating functions. To that purpose, a C*-algebra of sequences is introduced, which contains the special sequences of approximating operators we are interested in. There is a direct relationship between the applicability of the approximation method to a given operator and invertibility of the corresponding sequence in this C*-algebra. Exploring this relationship, applicability criteria are derived by the use of C*-algebra and Banach algebra techniques (essentialization, localization andidentification of the local algebras by means of construction of locally equivalent representations). Finally, examples are presented, including explicit conditions for the applicability of spline Galerkin methods to Wiener-Hopf operators with piecewise continuous symbols. 相似文献
5.
M. Yahdi 《Proceedings of the American Mathematical Society》2006,134(9):2613-2620
The aim of this work is to study operators naturally connected to Ergodic operators in infinite-dimensional Banach spaces, such as Uniform-Ergodic, Cesaro-bounded and Power-bounded operators, as well as stable and superstable operators. In particular, super-Ergodic operators are introduced and shown to be strictly between Ergodic and Uniform-Ergodic operators, and that any power bounded operator is super-Ergodic in a superreflexive space. New relationships between these operators are shown, others are proven to be optimal or can be ameliorated according to structural properties of the Banach space, such as the superreflexivity or with unconditional basis.
6.
该文讨论了单位圆盘上不同Bers型空间之间的加权复合算子的有界性、紧性和弱紧性, 给出了一些充分必要的判别条件, 特别地得到不同Bers型空间上加权复合算子的紧性与弱紧性的等价性. 这些推广了经典的复合算子与乘法算子的相关结论. 该文同时也给出了Bers型空间上复合算子的Fredholm性和闭值域问题的刻画, 完善了文献[6]中结论. 相似文献
7.
We study convolution type operators with kernels that have Fourier transforms in the class of piecewise continuous matrix functions. These convolution operators are assumed to act between Sobolev spaces defined on a union of a finite and a semi-infinite intervel. The main result is a criterion for the Fredholm property of these operators. An application to a problem related to diffraction theory is illustrated. 相似文献
8.
Denote by W(A) the numerical range of a bounded linear operator A. For two operators A and B (which may act on different Hilbert spaces), we study the relation between the inclusion relation W(A)⊆W(B) and the condition that A can be dilated to an operator of the form B⊗I. We also investigate the possibilities of dilating an operator A to operators with simple structure under the assumption that W(A) is included in a special region. 相似文献
9.
Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2007,327(1):257-268
This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties. 相似文献
10.
This paper is devoted to the question to obtain (algebraic and topologic) equivalence (after extension) relations between convolution type operators on unions of intervals and convolution type operators on the half-line. These operators are supposed to act between Bessel potential spaces,H
s,p
, which are the appropriate spaces in several applications. The present approach is based upon special properties of convenient projectors, decompositions and extension operators and the construction of certain homeomorphisms between the kernels of the projectors. The main advantage of the method is that it provides explicit operator matrix identities between the mentioned operators where the relations are constructed only by bounded invertible operators. So they are stronger than the (algebraic) Kuijper-Spitkovsky relation and the Bastos-dos Santos-Duduchava relation with respect to the transfer of properties on the prize that the relations depend on the orders of the spaces and hold only for non-critical orders:S – 1/p . For instance, (generalized) inverses of the operators are explicitly represented in terms of operator matrix factorization. Some applications are presented.This research was supported by Junta Nacional de Investigação Científica e Tecnológica (Portugal) and the Bundesminister für Forschung und Technologie (Germany) within the projectSingular Operators-new features and applications, and by a PRAXIS XXI project under the titleFactorization of Operators and Applications to Mathematical Physics. 相似文献
11.
Julio Flores 《Journal of Mathematical Analysis and Applications》2008,343(2):743-751
It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators. 相似文献
12.
Lanzhe Liu 《Proceedings Mathematical Sciences》2004,114(3):235-251
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue
spaces to Orlicz spaces are obtained. The operators include Calderón—Zygmund singular integral operator, fractional integral
operator, Littlewood—Paley operator and Marcinkiewicz operator. 相似文献
13.
This paper focuses on boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships with other two important induced linear operators are established. Several characterizations for closedness, closability, bundedness, relative boundedness and boundedness from below (above) of linear relations are given in terms of their induced linear operators. In particular, the closed graph theorem for linear relations in Banach spaces is completed, and stability of closedness of linear relations under bounded and relatively bounded perturbations is studied. The results obtained in the present paper generalize the corresponding results for single-valued linear operators to multi-valued linear operators, and some improve or relax certain assumptions of the related existing results. 相似文献
14.
本文在Banach空间中引入一类H-增生算子的混合拟变分包含,并提出求该变分包含问题解的邻近点法.通过H-增生算子的预解算子技术,建立了混合拟变分包含问题与邻近算子方程的等价关系,由这个等价关系得到求解邻近算子方程的迭代算法,该算法收敛于上述混合拟变分包含问题的解. 相似文献
15.
A.P. Nolasco 《Journal of Mathematical Analysis and Applications》2007,331(1):329-341
This paper presents a Duduchava-Saginashvili's type theory for Wiener-Hopf plus Hankel operators with semi-almost periodic Fourier symbols and acting between Lp Lebesgue spaces. This means the obtainment of one-sided invertibility and Fredholm property for these operators upon certain mean values of the representatives at infinity of their Fourier symbols. Additionally, a formula for the Fredholm index is provided by introducing a corresponding winding number of some new elements. 相似文献
16.
林鸿钊 《纯粹数学与应用数学》2011,27(5):650-655
为了进一步研究Banach空间中集合的紧致性,受极限集与极限算子定义的启发,给出了弱极限集与弱极限算子的定义,得到了它们的等价刻画,利用空间结构与算子理想的互动关系证明了弱极限算子全体是Pietsch意义下的闭满射算子理想. 相似文献
17.
一类次线性算子在广义Morrey空间上的加权有界性 总被引:1,自引:0,他引:1
本证明了如果次线性算子T在Orlicz空间上有介,则也有Morrey空间上有界,该算子包括极大算子和奇异积分算子等重要算子。 相似文献
18.
Derek Kitson 《Journal of Mathematical Analysis and Applications》2011,378(2):680-686
Recent contributions on spaceability have overlooked the applicability of results on operator range subspaces of Banach spaces or Fréchet spaces. Here we consider general results on spaceability of the complement of an operator range, some of which we extend to the complement of a union of countable chains of operator ranges. Applications we give include spaceability of the non-absolutely convergent power series in the disk algebra and of the non-absolutely p-summing operators between certain pairs of Banach spaces. Another application is to ascent and descent of countably generated sets of continuous linear operators, where we establish some closed range properties of sets with finite ascent and descent. 相似文献
19.
The connection between similarity logic and the theory of closure operators is examined. Indeed one proves that the consequence relation defined in [14] can be obtained by composing two closure operators and that the resulting operator is still a closure operator. Also, we extend any similarity into a similarity which is compatible with the logical equivalence, and we prove that this gives the same consequence relation. 相似文献
20.
卜庆营 《纯粹数学与应用数学》1997,13(1):47-49
A.Pietsch^[1]在讨论核局部凸空间时给出了两类矢值序列空间l1[X]和l1{X}。本文建立了矢值序列空间l1[X]及l1{X}和连续线性算子空间L(c0,X)及绝对可和算子空间AS(c0,X)之间的拓扑同胚关系。通过c0上的矢值算子类L(c0,X)和AS(c0,X)及其上的拓扑等价关系,对局部凸空间X是核空间给出了一个新的特征刻划。 相似文献