Calderón-Zygmund Operators on the Predual of a Morrey Space

We consider the boundedness of Calderón-Zygmund operators from H ^{p ,ϕ} (R ⁿ )(the predual of a Morrey space) to h ^{p ,ϕ} (R ⁿ )(the local version of H ^{p ,ϕ} ). We show that Calderón's commutator is bounded from H ^{p ,ϕ} to h ^{p ,ϕ} .     

Compactness of Product Operators on the Bergman Space

In this paper, we study the compactness of the product of a composition operator with another one＇s adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given.     

Spatiality of Derivations on the Algebra of τ-Compact Operators

This paper is devoted to derivations on the algebra S ₀(M, τ) of all τ-compact operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. The main result asserts that every t _τ -continuous derivation ${D : S_0(M, \tau) \rightarrow S_{0}(M, \tau)}$ is spatial and implemented by a τ-measurable operator affiliated with M, where t _τ denotes the measure topology on S ₀(M, τ). We also show the automatic t _τ -continuity of all derivations on S ₀(M, τ) for properly infinite von Neumann algebras M. Thus in the properly infinite case the condition of t _τ -continuity of the derivation is redundant for its spatiality.     

Decomposable Multipliers on a Banach Algebra

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Lipschitzian Operators of Substitution in the Algebra ΛBV

We present necessary and sufficient conditions on the generating functions of operators of substitution (=Nemytskii superposition operators), which map the Waterman space v BV of functions of v -bounded variation on the interval into another space of this type and satisfy the Lipschitz condition.     

Wolff’s Problem of Ideals in the Multiplier Algebra on Dirichlet Space

We establish an analogue of Wolff’s theorem on ideals in \(H^{\infty }(\mathbb {D})\) for the multiplier algebra of Dirichlet space.     

Strictly Cyclic Algebra of Operators Acting on Banach Spaces H p(β)

Let be a sequence of positive numbers and 1 p< . We consider the space H ^p() of all power series such that . We investigate strict cyclicity of the weakly closed algebra generated by the operator of multiplication by zacting on H ^p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on H ^p() when is strictly cyclic.     

Solutions of Equations Involving Analytic Functions in a Banach Algebra

By the properties of univalent analytic functions,we have discussed the exi-stence and uniqueness of eqation f(x)=a in a Banach algebra.We have the follo-wing fundamental lemmas. Lemma 1. Let A be a Banach algebra with identity e,W,U be two opensubsets of C, U W,f be an analytic function in W, and univalent in U, V=f(U),a∈A.If σ(a) V,then there exists unique x∈A such that σ(x) U {λ∈W|f(λ) V}and f(x)=a     

On the Ordered K0‐Group of Universal, Free Product C*‐Algebras

The ordered K₀-group of the universal, unital free product C^*-algebra M_k()*M_l()is calculated in the case where k is prime and not a divisor in l. It is shown that the positive cone of K₀(M_k()*M_l())is as small as possible in this case. The article also contains results (full and partial) on the ordered K₀0-group of more general universal, unital free product C^* algebras.     

Sequences of Weighted Composition Operators on the Hardy–Hilbert Space

Let \(\varphi \) be an analytic self map of the open unit disc \(\mathbb {D}\). Assume that \(\psi \) is an analytic map of \(\mathbb {D}\). Suppose that f is in the Hardy–Hilbert space of the open unit disc \(H^2\). The operator that takes f into \(\psi \cdot f \circ \varphi \) is a weighted composition operator, and is denoted by \(C_{\psi ,\varphi }\). In this paper we relate the convergence of the sequence \(\{ C_{\psi _n,\varphi _n}\}\) in different operator topologies to the convergence of the two sequences of maps \(\{\varphi _n \}\) and \(\{ \psi _n\}\).     

k-order Slant Toeplitz Operators on the Bergman Space

In this paper κ-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed.     

On Rubel’s Problem in the Class of Linear Operators on the Space of Analytic Functions

In this paper, we describe all derivation pairs of linear operators that act in spaces of functions analytic in domains.     

Reducing Subspaces of Certain Analytic Toeplitz Operators on the Bergman Space

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A Necessary and Sufficient Condition on Convergence of Bounded Linear Operators in the Space of Continuous Functions

Korovkin[1]gave a necessary and sufficient condition on lineax positiveapproximation in C[a,b].In this note,we give such a condition on general boundedapproximation in C[a,b]     

The Hypoellipticity for a Class of Convolution Operators on the Nilpotent Lie Group H_n■R~k

In this paper we discuss the hypoellipticity for a class of convolution operatorson the nilpotent Lie group H_nR~k(see [1]).The class of these operators containsall right invariant differential operators on H_nR~k,but it is far wider than later.We obtain some results which are an extension of the famous conclusions in[2]aboutleft invariant differential operators on general nilpotent Lie groups.     

On Completeness and Minimality of Random Exponential System in a Weighted Banach Space of Functions Continuous on the Real Line

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.     

Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space

We study convergence, rate of convergence and data dependency of normal?S iterative method for a fixed point of a discontinuous operator T on a Banach space. We also prove some Collage type theorems for T. The main aim here is to show that there is a close relationship between the concepts of data dependency of fixed points and the collage theorems and show that the latter provides better estimate. Numerical examples in support of the results obtained are also given.     

The Weighted Estimates of the Schrdinger Operators on the Nilpotent Lie Group

In this paper we consider the Schrdinger operator-△G + W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse Hlder class Bq1 for some q1 ≥ D2 and D is the dimension at infinity of G.The weighted Lp-Lq estimates for the operators Wα(-△G + W)-β and Wα G(-△G + W)-β are obtained.