dc.contributor.advisor | Sanders, Bobby L. | |
dc.contributor.author | Harvey, James Ronald | en_US |
dc.date.accessioned | 2019-10-11T15:11:01Z | |
dc.date.available | 2019-10-11T15:11:01Z | |
dc.date.created | 1969 | en_US |
dc.date.issued | 1969 | en_US |
dc.identifier | aleph-254660 | en_US |
dc.identifier.uri | https://repository.tcu.edu/handle/116099117/33804 | |
dc.description.abstract | A 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.extent | iii, 31 leaves, bound | en_US |
dc.format.medium | Format: Print | en_US |
dc.language.iso | eng | en_US |
dc.relation.ispartof | Texas Christian University dissertation | en_US |
dc.relation.ispartof | AS38.H37 | en_US |
dc.subject.lcsh | Banach spaces | en_US |
dc.title | Sequence spaces and the basis concept in Banach spaces | en_US |
dc.type | Text | en_US |
etd.degree.department | Department of Mathematics | |
etd.degree.level | Doctoral | |
local.college | College of Science and Engineering | |
local.department | Mathematics | |
local.academicunit | Department of Mathematics | |
dc.type.genre | Dissertation | |
local.subjectarea | Mathematics | |
dc.identifier.callnumber | Main Stacks: AS38 .H37 (Regular Loan) | |
dc.identifier.callnumber | Special Collections: AS38 .H37 (Non-Circulating) | |
etd.degree.name | Doctor of Philosophy | |
etd.degree.grantor | Texas Christian University | |