$p$-Dual frames and $p$-Riesz sequences in quasinormed spaces

José Alfonso López Nicolás

doi:10.33044/revuma.v61n2a07

Abstract

The present contribution is aimed at obtaining new results in duality between-dual frames and p-Riesz sequences in quasinormed spaces with a normalized Schauder basis. We obtain two results which show the relationship of duality between these concepts. We split a quasinormed space into a topological sum of two subspaces and use the Schauder basis to establish a relationship between the p-dual frames of one of these subspaces and the p-Riesz sequences of the dual of the other one. In fact, the main results are stated in a lightly more general context.

Highlights

In 1946 Gabor introduced a fundamental approach to signal decomposition in terms of elementary signals
In 1991 Grochenig defined Banach frames for a Banach space X with respect to an associated Banach space Xd of scalar valued sequences indexed by N: Definition 1.1 (Grochenig, [9])
Let X be a Banach space and let Xd be an associated Banach space of scalar valued sequences indexed by N

Summary

Introduction

In 1946 Gabor introduced a fundamental approach to signal decomposition in terms of elementary signals (see [8]). P-DUAL FRAMES AND p-RIESZ SEQUENCES IN QUASINORMED SPACES 293

Objectives

Results

Conclusion