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DC Field | Value | Language |
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dc.contributor.advisor | Husain, T. | en_US |
dc.contributor.author | El-Helaly, Taha Sherif | en_US |
dc.date.accessioned | 2014-06-18T16:33:15Z | - |
dc.date.available | 2014-06-18T16:33:15Z | - |
dc.date.created | 2010-05-10 | en_US |
dc.date.issued | 1985-08 | en_US |
dc.identifier.other | opendissertations/1202 | en_US |
dc.identifier.other | 2498 | en_US |
dc.identifier.other | 1304001 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/5856 | - |
dc.description.abstract | <p>An M-basis in a topological vector space is a special case of the extended Markushevich basis, and a generalization of the unconditional basis. We study orthogonal bases and orthogonal M-bases in topological algebras, with emphasis on locally convex algebras. It turns out that an orthogonal basis or an orthogonal M-basis in a topological algebra is necessarily Schauder. We characterize some concrete topological algebras with orthogonal bases or orthogonal M-bases, up to a topological isomorphism. We introduce and study two classes of locally convex algebras: the class of "Φ-algebras" which includes, for example ℂʳ, c₀(r), C*₃(r) and H(D) (with the Hadamard multiplication); and the larger class of "locally convex s-algebras" which also includes - among other examples - ℓp, 1 ≤ p < ∞ and the Arens algebra L^ω[0,1]. A Φ-algebras is not necessarily locally m-convex, and a locally m-convex algebra is not necessarily a locally convex s-algebra. We give two examples of Banach algebras with orthogonal bases which are not unconditional and we prove that an orthogonal basis in a B₀ algebra is unconditional iff the algebra is a locally convex s-algebra. We also study the conversion of a Fréchet space with an unconditional basis into a Fréchet algebra with the basis under consideration as an orthogonal basis and we obtain a necessary and sufficient condition for this to be possible, revising and extending a result of Husain and Watson obtained for Banach spaces.</p> | en_US |
dc.subject | Mathematics | en_US |
dc.subject | Mathematics | en_US |
dc.title | Topological Algebras with Orthogonal M-bases | en_US |
dc.type | thesis | en_US |
dc.contributor.department | Mathematics | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
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fulltext.pdf | 2.06 MB | Adobe PDF | View/Open |
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