A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...

A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We fin...

In this paper we study the average distance in weighted graphs. More precisely, we consider assignments of families of non-negative weights to the edges. The aim is to maximise (minimise, respectively) the average distance in the resulting weighted graph. Two variants of the problem are considered depending on whether the collection of weights is fixed or not. The main results of this paper are...

Abstract In this study, we deal with some new vector valued multiplier spaces $S_{G_{h}}(\sum_{k}z_{k})$ SGh(?kzk<mml:mo...

Abstract In this survey we report about recent work on weighted Banach spaces of analytic functions the unit disc and whole complex plane defined with sup-norms operators between them. Results solid hull core these distance formulas are reviewed. Differentiation integration operators, Cesàro Volterra composition superposition Toeplitz analyzed. Boundedness, compactness, spectrum, hypercyclicity...