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New identity on Parseval p-approximate Schauder frames and applications
(Taru Publications, 2021) Mahesh Krishna, K.; Johnson, P.
A very useful identity for Parseval frames for Hilbert spaces was obtained by Balan, Casazza, Edidin, and Kutyniok. In this paper, we obtain a similar identity for Parseval p-approximate Schauder frames for Banach spaces which admits a homogeneous semi-inner product in the sense of Lumer-Giles. © 2021 Taru Publications.
MULTIPLIERS FOR LIPSCHITZ p?BESSEL SEQUENCES IN METRIC SPACES
(Kyungnam University Press, 2025) Mahesh Krishna, K.; Johnson, P.; Harikrishnan, H.
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 how variations in the parameters of the multiplier affect its properties. © 2025, Kyungnam University Press. All rights reserved.