MULTIPLIERS FOR LIPSCHITZ p-BESSEL SEQUENCES IN METRIC SPACES

Abstract

The notion of multipliers in Hilbert spaces was introduced by Schatten in 1960 using orthonormal sequences, and it was generalized by Balazs in 2007 using Bessel sequences.This concept was further extended to Banach spaces by Rahimi and Balazs in 2010 using p-Bessel sequences. In this paper, we extend this framework by considering Lipschitz functions. Along the way, we define frames for metric spaces, thereby generalizing the notion of frames and Bessel sequences for Banach spaces. We show that when the symbol sequence converges to zero, the associated multiplier is a Lipschitz compact operator. Finally, we study howvariations in the parameters of the multiplier affect its properties