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1.
In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces.  相似文献   

2.
We consider composition operators on spaces of analytic functions. First we give an elementary proof for the well-known fact that these operators are bounded on the usual Hardy spaces. Then, for more general spaces, we give two results concerning the question when composition operators are injective or onto, and get a complete answer for a class of spaces, including the Hardy spaces.  相似文献   

3.
We study module spaces for linear relations (multi-valued operators) in a Hilbert space. The defect spaces are not required to be finite-dimensional. In particular we pay attention to module spaces for symmetric relations.  相似文献   

4.
In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and more generally to weighted Fock spaces.  相似文献   

5.
In this paper we consider a class of weighted integral operators onL 2 (0, ) and show that they are unitarily equivalent to Hankel operators on weighted Bergman spaces of the right half plane. We discuss conditions for the Hankel integral operator to be finite rank, Hilbert-Schmidt, nuclear and compact, expressed in terms of the kernel of the integral operator. For a particular class of weights these operators are shown to be unitarily equivalent to little Hankel operators on weighted Bergman spaces of the disc, and the symbol correspondence is given. Finally the special case of the unweighted Bergman space is considered and for this case, motivated by approximation problems in systems theory, some asymptotic results on the singular values of Hankel integral operators are provided.  相似文献   

6.
In the paper, we give characterizations of Hankel operators on generalizedH 2 spaces and obtain some properties for corresponding Hankel algebras.Supported in part by NSF of China  相似文献   

7.
The characterization of thosef for which the Hankel operatorsH f belongs to various trace ideals over Bergman spaces on pseudoconvex domains of finite type in complex dimension two is given. In particular, we determine how the cutoff values are affected by the boundary geometry.All three authors supported by grants from the National Science Foundation  相似文献   

8.
In this paper we establish several new results on the existence and uniqueness of a fixed point for holomorphic mappings and one-parameter semigroups in Banach spaces. We also present an application to operator theory on spaces with an indefinite metric.  相似文献   

9.
We study the commutator of the multiplication and harmonic Bergman projection, Hankel and Toeplitz operators on the harmonic Bergman spaces. The same type operators have been well studied on the analytic Bergman spaces. The main difficulty of this study is that the bounded harmonic function space is not an algebra! In this paper, we characterize theL p boundedness and compactness of these operators with harmonic symbols. Results about operators in Schatten classes, the cut-off phenomenon and general symbols are also included.Partially supported by a grant from the Research Grants Committee of the University of Alabama.  相似文献   

10.
We study differences of weighted composition operators between weighted Banach spaces H ν of analytic functions with weighted sup-norms and give an expression for the essential norm of these differences. We apply our result to estimate the essential norm of differences of composition operators acting on Bloch-type spaces. Authors’ addresses: Mikael Lindstr?m, Department of Mathematics, Abo Akademi University, FIN 20500 Abo, Finland; Elke Wolf, Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany  相似文献   

11.
In the setting of K?the function spaces we present some suffcient conditions for a regular integral operator to be strictly singular.  相似文献   

12.
 In this paper we apply a time-frequency approach to the study of pseudodifferential operators. Both the Weyl and the Kohn–Nirenberg correspondences are considered. In order to quantify the time-frequency content of a function or distribution, we use certain function spaces called modulation spaces. We deduce a time-frequency characterization of the twisted product of two symbols σ and τ, and we show that modulation spaces provide the natural setting to exactly control the time-frequency content of from the time-frequency content of σ and τ. As a consequence, we discuss some boundedness and spectral properties of the corresponding operator with symbol . (Received 27 December 1999; in final form 9 November 2000)  相似文献   

13.
《Quaestiones Mathematicae》2013,36(4):549-561
Abstract

In this note we generalize a result of L. Weis and V. V. Shevchik about strict singularity of the Fourier transform to a large class of locally integral operators on function spaces.  相似文献   

14.
In this paper, we study the boundedness and the compactness of composition operators on Orlicz–Lorentz spaces.   相似文献   

15.
ABSTRACT

In this note we present a characterization of the band of kernel operators in the abstract setting of Riesz spaces. Under the assumptions that E is an Archimedean Riesz space and F a Dedekind complete Riesz space separated by its ex= tended order continuo88 dual, we obtain a characterization of the band (Eoo ? F)dd in terms of (sequentially) star or= der continuous operators.  相似文献   

16.
 In [9], Hedenmalm, Lindqvist and Seip introduce the Hilbert space of Dirichlet series with square summable coefficients , and begin its study, with modern functional and harmonic analysis tools. The space is an analogue for Dirichlet series of the space for Fourier series. We continue their study by introducing , an analogue to the spaces . Thanks to Bohr’s vision of Dirichlet series, we identify with the Hardy space of the infinite polydisk . Next, we study a variant of the Poisson semigroup for Dirichlet series. We give a result similar to the one of Weissler ([25]) about the hypercontractivity of this semigroup on the spaces . Finally, following [8], we determine the composition operators on , and we compare some properties of such an operator and of its symbol. Received October 3, 2001; in revised form January 16, 2002 Published online July 12, 2002  相似文献   

17.
In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on ?p spaces in fact hold true for mappings on arbitrary Banach spaces.  相似文献   

18.
《Mathematische Nachrichten》2017,290(2-3):349-366
In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.  相似文献   

19.
In this paper we obtain general infinite dimensional inertia theorems for linear pencils in Hilbert space which cover previously known results for the finite dimensional case and for block weighted shifts. Connections with definite subspaces for contractions in spaces with indefinite metric are discussed.  相似文献   

20.
We find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in CN. As a consequence we characterize the compactness of these operators. The boundedness of these operators is also characterized.  相似文献   

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