On unconditional section boundedness in sequence spaces

Abstract

SEMBER 1. Introduction. The concepts of section boundedness (A), section convergence (AK) and functional section convergence (FAK) have been of great interest in summability and in the study of topological sequence spaces. More general notions of Cesro-section boundedness and convergence and T-section boundedness and convergence have also been investigated and shown to be significant [2, 3]. The usual sections associated with a sequence x are the finite sequences at the front of x, that is, the sequences P n (x) = (x i9 x 2 , -, x n> 0, 0, ) = 2*=i x kS k -The purpose of this work is to investigate the topological significance in a sequence space of the set of unrestricted sections of a sequence x, that is, the set of all sequences having the form 2* F x k& k > where F is some finite subset of the positive integers.