Composition Operators on the Space of Bounded Harmonic Functions

We study composition operators on the space of bounded harmonic functions on the open unit disk. The principal goal of this paper is to provide criteria for determining the essential norm of difference of two composition operators. The third author is partially supported by Grant-in-Aid for Scientific Research (No.17540169), Japan Society for the Promotion of Science.     

Weighted Composition Operators on the Space of Bounded Harmonic Functions

We determine the norm and the essential norm of the difference of weighted composition operators on the space of bounded harmonic functions on the open unit disk. The argument is done on the boundary.     

连续函数空间上有界线性算子逼近的一个充要条件

Korovkin [1] gave a necessary and sufficient condition on linear positive approximation in C[a,b]. In this note, we give such a condition on general bounded approximation in C[a, b]     

Uniformly Bounded Composition Operators on the Space of Bounded Variation Functions in the Sense of Waterman

In this paper, we demonstrate under some general assumptions, that a generator of any uniformly bounded composition operator, mapping spaces of bounded variation (Waterman) functions into other spaces of this type, must be an affine function in the functional variable.

     

加权BMO函数空间上的Littlewood-Paley算子

Littlewood—Paley算子(g—函数,s—函数与_λ^*—函数,λ>3)作为BMO_w或(BMO)_w上的算子都是“有界的”,确切地说,我们证明了:若f∈BMO_w或(BMO)_w且|{x:Tf(x)≠∞}|>0,则Tf也属于BMO_w或(BMO)_w并且存在与f无关的常数C使‖Tf‖_BMOw<     

Multiplication Operators Between the Lipschitz Space and the Space of Bounded Functions on a Tree

In this paper, we characterize the bounded and the compact multiplication operators between the space of bounded functions on the set of vertices of a rooted infinite tree T and the Banach space of complex-valued Lipschitz functions on T. We also determine the operator norm and the essential norm for the bounded multiplication operators between these spaces and show that there are no isometries among such operators.     

Invertibility Conditions and Bounds for Spectra of Matrix Integral Operators

 Matrix integral operators are considered. Bounds for the spectrum are established. In particular, they give the invertibility conditions and estimates for the spectral radius. (Received 16 December 1998; in revised form 30 May 1999)     

Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem

Recently this author studied several merit functions systematically for the second-order cone complementarity problem. These merit functions were shown to enjoy some favorable properties, to provide error bounds under the condition of strong monotonicity, and to have bounded level sets under the conditions of monotonicity as well as strict feasibility. In this paper, we weaken the condition of strong monotonicity to the so-called uniform P ^*-property, which is a new concept recently developed for linear and nonlinear transformations on Euclidean Jordan algebra. Moreover, we replace the monotonicity and strict feasibility by the so-called R ₀₁ or R ₀₂-functions to keep the property of bounded level sets. This work is partially supported by National Science Council of Taiwan.     

Hankel Operators on Bounded Analytic Functions

For a domain in the complex plane and a bounded measurable function on , the generalized Hankel operator on is the operator of multiplication by followed by projection into . Under certain conditions on we show that either is compact or there is an embedded on which is bicontinuous. We characterize those 's for which is compact in the case that is a Behrens roadrunner domain.

     

Eigenvalue Asymptotics for Locally Perturbed Second-Order Differential Operators

We consider the appearance of discrete spectrum in spectralgaps of magnetic Schrödinger operators with electric backgroundfield under strong, localised perturbations. We show that forcompactly supported perturbations the asymptotics of the countingfunction of the occurring eigenvalues in the limit of a strongperturbation does not depend on the magnetic field nor on thebackground field.     

Bounded Berezin-Toeplitz Operators on the Segal-Bargmann Space

We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj?strand. We also obtain the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order three are in the Wiener algebra of Sj?strand. Our method of proofs is based on the pseudodifferential calculus and the heat flow determined by the phase function of the Bargmann transform. Supported by the JSPS Grant-in-Aid for Scientific Research #20540151.     

Bounded Cosine Functions Close to Continuous Scalar Bounded Cosine Functions

Let \({(C(t))_{t\in \mathbb R}}\) be a cosine function in a unital Banach algebra. We show that if \({\sup_{t\in \mathbb R}\Vert C(t)-c(t)\Vert < 2}\) for some continuous scalar bounded cosine function \({(c(t))_{t\in \mathbb R},}\) then the closed subalgebra generated by \({(C(t))_{t\in \mathbb R}}\) is isomorphic to \({\mathbb C^k}\) for some positive integer k. If, further, \({\sup_{t\in \mathbb R}\Vert C(t)-c(t)\Vert < \frac{8}{3\sqrt 3},}\) then \({C(t)=c(t)}\) for \({t\in \mathbb R}\).     

Hilbert空间中有界线性算子的膨胀

在Hilert空间中,有界线性算子的膨胀概念是算子的扩张概念的推广。它在讨论压缩算子的不变子空间时是有用的(见[1])。本文的目的是给出Hilbert空间上的有界线性算子B是它的闭子空间上的有界线性算子A的膨胀的一个充要条件。并且利用它给出恰当膨胀和拟恰当膨胀的概念、当讨论的是压缩算子的保范膨胀和酉膨胀时,它们是分别和极小保范膨胀和极小酉膨胀相当的。     

A Superconsistent Chebyshev Collocation Method for Second-Order Differential Operators

A standard way to approximate the model problem –u =f, with u(±1)=0, is to collocate the differential equation at the zeros of T _n : x _i , i=1,...,n–1, having denoted by T _n the nth Chebyshev polynomial. We introduce an alternative set of collocation nodes z _i , i=1,...,n–1, which will provide better numerical performances. The approximated solution is still computed at the nodes {x _i }, but the equation is required to be satisfied at the new nodes {z _i }, which are determined by asking an extra degree of consistency in the discretization of the differential operator.     

Some Equivalent Conditions for the Differentiability of Continuous Gauge Functions on Banach Space

In this paper,some equivalent conditions for differentiability of condtinuous gauge function are given.     

Sufficient Conditions for Bounded Turning of Analytic Functions

Ukrainian Mathematical Journal - Consider a function f analytic in the open unit disk and normalized so that f(0) = f′(0) ? 1 = 0. The methods of the theory of first-order differential...