Unbounded Weighted Composition Operators on Fock space

Potential Analysis - The pluripolar hull of a pluripolar set E in ?n is the intersection of all complete pluripolar sets in ?n that contain E. We prove that the pluripolar hull of each...     

Products of Conditional Expectation Operators: Convergence and Divergence

Journal of Theoretical Probability - In this paper, we investigate the convergence of products of conditional expectation operators. We show that if $$(\Omega ,\mathcal {F},P)$$ is a probability...     

Unbounded Toeplitz Operators

This partly expository article develops the basic theory of unbounded Toeplitz operators on the Hardy space H ², with emphasis on operators whose symbols are not square integrable. Unbounded truncated Toeplitz operators on coinvariant subspaces of H ² are also studied. In memory of Paul R. Halmos     

Unbounded Quasinormal Operators Revisited

Various characterizations of unbounded closed densely defined operators commuting with the spectral measures of their moduli are established. In particular, Kaufman’s definition of an unbounded quasinormal operator is shown to coincide with that given by the third-named author and Szafraniec. Examples demonstrating the sharpness of results are constructed.     

关于条件期望的注记

利用条件期望的定义和性质给出了两个例子说明随机变量序列的条件期望唯一存在的情况.     

Unbounded Hankel Operators and Moment Problems

This note presents a matricial generalization of the concept of rigid functions in the Hardy space H¹, and a spectral characterization of complete non-determinacy for multivariate stationary processes.     

Ideals in Algebras of Unbounded Operators

A general procedure is given to get ideals in algebras of unbounded operators starting with ideals in ??(??). Algebraical and topological properties of ideals obtained in this manner from the well-known symmetrically-normed ideals S_?(??) are described.     

The Density Problem for Unbounded Bergman Operators

The unbounded Bergman operator, the operator of multiplication by on an unbounded open subset of the plane, is considered. We give a complete answer regarding the density problem of unbounded Bergman operators in terms of its equivalence to the problem of bounded point evaluations for the Bergman spaces. Using this equivalence and the notion of Wiener capacity, we obtain simple geometric conditions that classify almost those open subsets of the plane for which the corresponding Bergman operators are densely defined. With the aid of an analytic approach, we are also able to give condition for a large collection of open subsets of the plane for which all the positive integer powers of the corresponding Bergman operators are densely defined. Submitted: December 14, 2001? Revised: January 14, 2001.     

Weighted Composition Operators on Weighted Dirichlet Spaces

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Carleson measure.     

Spectral Inclusion Properties of Unbounded Hamiltonian Operators

In this paper, the authors investigate the spectral inclusion properties of the quadratic numerical range for unbounded Hamiltonian operators. Moreover, some examples are presented to illustrate the main results.     

On Weighted L~p-Approximation by Weighted Bernstein-Durrmeyer Operators

In the present paper,we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted L~p-norm with Jacobi weight w(x) = x~α(1-x)~β.All the results involved have no restriction α,β 1-1/p,which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.     

Segal-Bargmann空间上带无界符号的Toeplitz算子

In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H2(Cn,d Vα).     

一类无界算子的Weyl定理

研究了一类无界算子的Weyl定理,刻画了具有扰动的无界自伴算子的Weyl定理.     

Conditional Expectation Depending on a Parameter And Strong Holomorphic Conditional Probability

In this paper,we have given the existence theorem of the conditional expectation depending pa-rameter and the existence theorem of the strong holomorphic conditional probability,and another a few ralated theorems.These results are to approach one of addition for correlated components in the probabil-ity theory and the measure theory.     

Generalized Weighted Composition Operators on Weighted Bergman Spaces

The boundedness and compactness of the generalized weighted composition operator on weighted Bergman spaces are discussed.     

Approximation of Unbounded Functions by Linear Positive Operators

A unified class of linear positive operators has been defined. Using these operators some approximation estimates have been obtained for unbounded functions. For particular linear positive operators these results sharpen and improve the earlier estimates due to Fuhua Cheng (J. Approx. Theory, 1984) and Xiehua Sun (J. Approx. Theory, 1988).     

无界形式Hamilton算子的可逆性

利用算子分块方法研究了具有一般定义域的形式Hamilton算子的可逆性和可逆补,还进一步给出了无穷维Hamilton算子的相关结论.     

On Some Product of Two Unbounded Self-Adjoint Operators

We give a spectral analysis of some unbounded normal product HK of two self-adjoint operators H and K (which appeared in [7]) and we say why it is not self-adjoint even if the spectrum of one of the operators is sufficiently “asymmetric”. Then, we investigate the self-adjointness of KH (given it is normal) for arbitrary self-adjoint H and K by giving a counterexample and some positive results and hence finishing off with the whole question of normal products of self-adjoint operators (appearing in [1, 7, 12]). The author was supported in part by CNEPRU: B01820070020 (Ministry of Higher Education, Algeria).