Show simple item record

dc.contributor.advisorSanders, Bobby L.
dc.contributor.authorHarvey, James Ronalden_US
dc.date.accessioned2019-10-11T15:11:01Z
dc.date.available2019-10-11T15:11:01Z
dc.date.created1969en_US
dc.date.issued1969en_US
dc.identifieraleph-254660en_US
dc.identifier.urihttps://repository.tcu.edu/handle/116099117/33804
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.language.isoengen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.relation.ispartofAS38.H37en_US
dc.subject.lcshBanach spacesen_US
dc.titleSequence spaces and the basis concept in Banach spacesen_US
dc.typeTexten_US
etd.degree.departmentDepartment of Mathematics
etd.degree.levelDoctoral
local.collegeCollege of Science and Engineering
local.departmentMathematics
local.academicunitDepartment of Mathematics
dc.type.genreDissertation
local.subjectareaMathematics
dc.identifier.callnumberMain Stacks: AS38 .H37 (Regular Loan)
dc.identifier.callnumberSpecial Collections: AS38 .H37 (Non-Circulating)
etd.degree.nameDoctor of Philosophy
etd.degree.grantorTexas Christian University


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record