Sanders, Bobby L.2019-10-112019-10-1119691969https://repository.tcu.edu/handle/116099117/33804A sequence of vectors, (x_n), in a Banach space E is a basis for E if there exists a sequence (X_n) of linear functionals on E such that the following conditions hold; (i)x = Summation of X_n(x)x_n for all x in E, (ii) X_n is continuous for each n, (iii) (x_n) is biorthogonal to (X_n). If (x_n) is any sequence of non-zero vectors in E then S = {(a_n) : Summation of a_n x_n converges in E} is a Banach space. This dissertation investigates the properties of S that imply the existence of linear functionals on E such that one or more of the above conditions hold.iii, 31 leaves, boundFormat: PrintengBanach spacesTextMain Stacks: AS38 .H37 (Regular Loan)Special Collections: AS38 .H37 (Non-Circulating)