$(X_{d}, X_{d}^{*})$-Bessel multipliers in Banach spaces

Multipliers of pg-Bessel sequences in Banach spaces

In this paper, we introduce $(p,q)g-$Bessel multipliers in Banach spaces and we show that under some conditions a $(p,q)g-$Bessel multiplier is invertible. Also, we show the continuous dependency of $(p,q)g-$Bessel multipliers on their parameters.

Abel-schur Multipliers on Banach Spaces of Infinite Matrices

We consider a more general class than the class of Schur multipliers namely the Abel-Schur multipliers, which in turn coincide with the bounded linear operators on `2 preserving the diagonals. We extend to the matrix framework Theorem 2.4 (a) of a paper of Anderson, Clunie, and Pommerenke published in 1974, and as an application of this theorem we obtain a new proof of the necessity of an old t...

Multipliers and Toeplitz Operators on Banach Spaces of Sequences

In this paper, we prove that every multiplier M (i.e. every bounded operator commuting whit the shift operator S) on a large class of Banach spaces of sequences on Z is associated to a function essentially bounded by ‖M‖ on spec(S). This function is holomorphic on ◦ spec(S), if ◦ spec(S) 6= ∅. Moreover, we give a simple description of spec(S). We also obtain similar results for Toeplitz operato...

Bessel, Frame and Riesz Multipliers

Abstract. This paper introduces the concept of Bessel and frame multipliers. These operators are defined by a fixed pattern, called the symbol, which is used after analysis, before synthesis. This concept is a generalization of Gabor multipliers. It allows specialization to any analysis/synthesis systems, that form Bessel sequences, like e.g. wavelet frames. Basic properties of this general cla...

Multipliers of generalized frames in Hilbert spaces