About Schauder frames and besselian Schauder frames of Banach spaces

TL;DR

This paper introduces new concepts of besselian pairs and besselian Schauder frames in separable Banach spaces, establishing fundamental theoretical results about their properties.

Contribution

It presents novel definitions and foundational results for besselian pairs and Schauder frames in Banach spaces, expanding the theoretical framework.

Findings

Introduction of besselian pairs and Schauder frames

Proven fundamental properties of these new notions

Extended the theoretical understanding of Banach space frames

Abstract

In this paper, we introduce, for a separable Banach spacea new notion of besselian paires and of besselian Schauder frames for which we prove for some fundamental results.