Multipliers for p-Bessel sequences in Banach spaces

TL;DR

This paper generalizes the concept of multipliers from Hilbert spaces to Banach spaces, analyzing their boundedness, compactness, nuclearity, and parameter dependence for p-Bessel and p-Riesz sequences.

Contribution

It extends the theory of multipliers to Banach spaces, providing conditions for boundedness, compactness, nuclearity, and continuity of these operators.

Findings

Bounded symbols produce bounded multipliers.

Symbols tending to zero induce compact operators.

Conditions for multipliers to be nuclear operators.

Abstract

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.