On various Riesz-dual sequences for Schauder frames

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.