On various Riesz-dual sequences for Schauder frames

Ali Reza Neisi; Mohammad Sadegh Asgari

doi:10.1016/j.heliyon.2020.e04963

On various Riesz-dual sequences for Schauder frames

Heliyon. 2020 Sep 21;6(9):e04963. doi: 10.1016/j.heliyon.2020.e04963. eCollection 2020 Sep.

Authors

Ali Reza Neisi¹, Mohammad Sadegh Asgari¹

Affiliation

¹ Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P. O. Box 13185/768, Tehran, Iran.

Abstract

In this paper, we introduce various definitions of R-duals, to be called R-duals of type I, II, which leads to a generalization of the duality principle in Banach spaces. A basic problem of interest in connection with the study of R-duals in Banach spaces is that of characterizing those R-duals which can essentially be regarded as M-basis. We give some conditions under which an R-dual sequence to be an M-basis for X.

Keywords: Markushevich basis; Mathematics; Riesz basis; Riesz-dual sequence; Schauder frame.