Two different Topologies on the Dual of a Hilbert Space and the Merits of each of them
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Date
AUGUST, 2009
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Abstract
In this work we considered two topologies of a Hilbert space . The first one was its normed vector space topology, which is its natural topology. The second was its weak topology.
Among other properties we show that the closed unit ball is not compact when is given its topology as a Banach space. On the other hand is compact when is given its weak topology.
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A thesis
submitted to the board of Postgraduate Studies, Kwame Nkrumah University of Science and Technology (Knust), Kumasi, Ghana, in partial fulfillment of the requirements for the award of the Degree of Master of Science (Msc) In
Mathematics