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1.
Characterizations of g-frames and g-Riesz bases in Hilbert spaces   总被引:3,自引:0,他引:3  
In this paper, we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space, which will play a key role in studying g-frames and g-Riesz bases etc. Using the pre-frame operator Q, we give some necessary and sufficient conditions for a g-Bessel sequence, a g-frame, and a g-Riesz basis in a complex Hilbert space, which have properties similar to those of the Bessel sequence, frame, and Riesz basis respectively. We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis. Lastly, we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.  相似文献   

2.
李鹏同  鲁世杰 《东北数学》2002,18(4):323-329
Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.  相似文献   

3.
In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.  相似文献   

4.
This paper proves that a necessary condition for a composition operator on the Bloch space of the unit disk to be bounded below given by Ghatage, Yan and Zheng is also sufficient. Given furthermore are a sufficient condition and a necessary condition of the boundedness from below for a composition operator on the Bloch space of a unit ball with dimensions bigger than one.  相似文献   

5.
邓冠铁 《东北数学》2004,20(3):303-308
In this paper, we obtain a necessary and sufficient condition for the incompleteness of complex exponential system in Cα, where Cα is a weighted Banach space of complex continuous functions f on the real axis R with f(t) exp{-α(t)}vanishing at infinity, in the uniform norm.  相似文献   

6.
On the supercyclicity and hypercyclicity of the operator algebra   总被引:1,自引:0,他引:1  
Let B(X) be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or *-strong topology. We give sufficient conditions for a continuous linear mapping L : B(X) →B(X) to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied' by Chan and here we obtain an analogous result in the case of *-strong operator topology.  相似文献   

7.
In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.  相似文献   

8.
In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory.  相似文献   

9.
LIU  Chun-tai 《数学季刊》2013,(4):503-509
The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.  相似文献   

10.
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ.  相似文献   

11.
In this paper, we give some new results on sum and stability of g-frames in Hilbert spaces. Since the finite sum of g-frames may not be a g-frame for the Hilbert space, we give a necessary and sufficient condition and some sufficient conditions for the finite sum of g-frames to be a g-frame. We also show that every g-sequence in Hilbert space can be expanded to a tight g-frame by adding a linear bounded operator. Moreover, we obtain some sufficient conditions under which g-frames (and the finite sum of g-frames) are stable under small perturbations.  相似文献   

12.
Hilbert C~*-模上的广义g-框架   总被引:1,自引:0,他引:1  
本文主要研究了Hilbert C~*-模上广义g-框架.给出了Hilbert C~*-模上的广义g-框架,广义g-框架算子,广义典则对偶g-框架及广义交错对偶g-框架的定义,并证明了有关广义g-框架的一些结果.  相似文献   

13.
Exact g-frames in Hilbert spaces   总被引:2,自引:0,他引:2  
G-frames, which were considered recently as generalized frames in Hilbert spaces, have many properties similar to those of frames, but not all the properties are similar. For example, exact frames are equivalent to Riesz bases, but exact g-frames are not equivalent to g-Riesz bases. In this paper, we firstly give a characterization of an exact g-frame in a complex Hilbert space. We also obtain an equivalent relation between an exact g-frame and a g-Riesz basis under some conditions. Lastly we consider the stability of an exact g-frame for a Hilbert space under perturbation. These properties of exact g-frames for Hilbert spaces are not similar to those of exact frames.  相似文献   

14.
In this paper, we give a necessary and sufficient condition that a locally biholomorphic mapping f on the unit ball B in a complex Hilbert space X is a biholomorphic convex mapping, which improves some results of Hamada and Kohr and solves the problem which is posed by Graham and Kohr. From this, we derive some sufficient conditions for biholomorphic convex mapping. We also introduce a linear operator in purpose to construct some concrete examples of biholomorphic convex mappings on B in Hilbert spaces. Moreover, we give some examples of biholomorphic convex mappings on B in Hilbert spaces.  相似文献   

15.
在Hilbert空间中把斜对偶原理推广到更一般的g-框架.我们给出了{A_j:j∈J}是g-框架{F_j:j∈J}的一个斜对偶g-框架的等价条件,还给出了一个斜对偶g-框架对是对称的充分条件.最后,在不同的条件下构造了几对斜对偶g-框架.  相似文献   

16.
In this paper we show that every g-frame for an infinite dimensional Hilbert space H can be written as a sum of three g-orthonormal bases for H. Also, we prove that every g-frame can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. Further, we show each g-Bessel multiplier is a Bessel multiplier and investigate the inversion of g-frame multipliers. Finally, we introduce the concept of controlled g-frames and weighted g-frames and show that the sequence induced by each controlled g-frame (resp., weighted g-frame) is a controlled frame (resp., weighted frame).  相似文献   

17.
In a separable Banach space E, we study the invariance of a closed set K under the action of the evolution equation associated with a maximal dissipative linear operator A perturbed by a quasi-dissipative continuous term B. Using the distance to the closed set, we give a general necessary and sufficient condition for the invariance of K. Then, we apply our result to several examples of partial differential equations in Banach and Hilbert spaces.  相似文献   

18.
In this paper, we prove some theorems on fuzzy sets. We first show that, in order to demonstrate that the equality of shadows ofA andB implies the equality ofA andB, it is necessary to assume thatA andB are closed and thatS H (A)=S H (B) for any closed hyperplane hyperplaneH. We also obtain a separation theorem for two convex fuzzy sets in a Hilbert space. Finally, we investigate results relating to minimax theorems for fuzzy sets. We obtain a necessary and sufficient condition for compactness.The authors wish to express their sincere thanks to Professor Hisaharu Umegaki for his invaluable suggestions and advice.  相似文献   

19.
In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.  相似文献   

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