2020/07/07 by K. Mahesh Krishna, Krishna, K. Mahesh, P. Sam Johnson +1
Mathematics · #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research #Advanced Banach Space Theory
paper · pdf · doi:10.48550/arxiv.2007.03209
The notion of multipliers in Hilbert space was introduced by Schatten in 1960 using orthonormal sequences and was generalized by Balazs in 2007 using Bessel sequences. This was extended to Banach spaces by Rahimi and Balazs in 2010 using p-Bessel sequences. In this paper, we further extend this by considering Lipschitz functions. On the way we define frames for metric spaces which extends the notion of frames and Bessel sequences for Banach spaces. We show that when the symbol sequence converges to zero, the multiplier is a Lipschitz compact operator. We study how the variation of parameters in the multiplier effects the properties of multiplier.