Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/8548
Title: | Fréchet Algebras with Schauder Bases |
Authors: | Liang, Jaung |
Advisor: | Husain, T. |
Department: | Mathematics |
Keywords: | Mathematics;Mathematics |
Publication Date: | Mar-1975 |
Abstract: | <p>Let A be a Fréchet algebra with the defining sequence {qn}n≥1 of seminorms and identity e. Let {xᵢ} be a Schauder basis in A. Then each xεA, can be written as: x = ᵢ∑₁αᵢxᵢ, where {αᵢ} is a unique sequence of complex numbers depending upon x. αᵢ's are called coordinate functionals or coefficients. This thesis is concerned with some relations among coefficients, seminorms and the identity, e of A. Further, it is shown that each multiplicative linear functional on A is continuous provided a certain condition is satisfied. Some of the results needed to prove the above results are shown to be true for Fréchet spaces. Finally, a representation theorem for Fréchet * - algebra is given.</p> |
URI: | http://hdl.handle.net/11375/8548 |
Identifier: | opendissertations/3745 4762 1708195 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 1.58 MB | Adobe PDF | View/Open |
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