Lipschitz p-Approximate Schauder Frames

TL;DR

This paper introduces Lipschitz p-approximate Schauder frames, a new framework for representing subsets of Banach spaces via Lipschitz functions, and characterizes their properties and duals.

Contribution

It defines and characterizes Lipschitz p-ASFs and their duals, extending the theory of metric frames in Banach spaces.

Findings

Complete characterization of Lipschitz p-ASFs and their duals.

Introduction of similarity concept for Lipschitz p-ASFs.

Use of canonical Schauder basis for classical sequence spaces.

Abstract

With the aim of representing subsets of Banach spaces as an infinite series using Lipschitz functions, we study a variant of metric frames which we call Lipschitz p-approximate Schauder frames (Lipschitz p-ASFs). We characterize Lipschitz p-ASFs and their duals completely using the canonical Schauder basis for classical sequence spaces. Similarity of Lipschitz p-ASF is introduced and characterized.