New Identity on Parseval p-Approximate Schauder Frames and Applications

TL;DR

This paper extends a known identity from Hilbert space frames to Banach space frames with semi-inner products, broadening the theoretical understanding and potential applications of Parseval p-approximate Schauder frames.

Contribution

It introduces a new identity for Parseval p-approximate Schauder frames in Banach spaces with semi-inner products, generalizing previous Hilbert space results.

Findings

Derived a novel identity for Banach space frames

Extended frame theory to semi-inner product spaces

Potential applications in Banach space analysis

Abstract

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.