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dc.contributor.advisorSanders, Bobby L.
dc.contributor.authorHarvey, James Ronalden_US
dc.description.abstractA 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.
dc.format.extentiii, 31 leaves, bounden_US
dc.format.mediumFormat: Printen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.subject.lcshBanach spacesen_US
dc.titleSequence spaces and the basis concept in Banach spacesen_US
dc.typeTexten_US of Mathematics
local.collegeCollege of Science and Engineering
local.academicunitDepartment of Mathematics
dc.identifier.callnumberMain Stacks: AS38 .H37 (Regular Loan)
dc.identifier.callnumberSpecial Collections: AS38 .H37 (Non-Circulating) of Philosophy Christian University

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