Towards characterizations of approximate Schauder frame and its duals for Banach spaces

TL;DR

This paper explores the properties and characterizations of approximate Schauder frames and their duals in Banach spaces, providing new insights into their structure, similarity, and orthogonality.

Contribution

It introduces new characterizations of approximate Schauder frames and their duals, including operator-theoretic criteria for similarity and orthogonality in Banach spaces.

Findings

Characterizations of ASF and dual frames under certain conditions

Operator-theoretic criteria for similarity of ASFs

Analysis of orthogonality of ASFs

Abstract

We begin the study of characterizations of recently defined approximate Schauder frame (ASF) and its duals for separable Banach spaces. We show that, under some conditions, both ASF and its dual frames can be characterized for Banach spaces. We also give an operator-theoretic characterization for similarity of ASFs. Our results encode the results of Holub, Li, Balan, Han, and Larson. We also address orthogonality of ASFs.