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    Zero Divisors and Linear Independence of Translates

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    Date
    2015-06-29
    Author
    Roman, Ahmed Hemdan
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    Abstract
    In this thesis we discuss linear dependence of translations which is intimately related to the zero divisor conjecture. We also discuss the square integrable representations of the generalized Wyle-Heisenberg group in $n^2$ dimensions and its relations with Gabor's question from Gabor Analysis in the light of the time-frequency equation. We study the zero divisor conjecture in relation to the reduced $C^*$-algebras and operator norm $C^*$-algebras. For certain classes of groups we address the zero divisor conjecture by providing an isomorphism between the the reduced $C^*$-algebra and the operator norm $C^*$-algebra. We also provide an isomorphism between the algebra of weak closure and the von Neumann algebra under mild conditions. Finally, we prove some theorems about the injectivity of some spaces as $mathbb{C}G$ modules for some groups $G$.
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    http://hdl.handle.net/10919/53956
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    • Masters Theses [19619]

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