Neisi Ali Reza, Asgari Mohammad Sadegh
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P. O. Box 13185/768, Tehran, Iran.
Heliyon. 2020 Sep 21;6(9):e04963. doi: 10.1016/j.heliyon.2020.e04963. eCollection 2020 Sep.
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 .
在本文中，我们引入了R对偶的各种定义，将其称为I型、II型R对偶，这导致了巴拿赫空间中对偶原理的推广。与巴拿赫空间中R对偶研究相关的一个基本有趣问题是刻画那些本质上可视为M基的R对偶。我们给出了一些条件，在这些条件下一个R对偶序列成为某个空间的M基。
