On the Merits of Two Different Topologies on the Dual of a Hilbert Space

Emmanuel Akweittey, Gabriel Obed Fosu, Ahmed Mubarrack


Two topologies of a Hilbert space l 2 is considered in this work. To wit normed
vector space, which is its natural topology and weak topology. Among other properties we showed that the closed unit ball S is not compact when l 2is given its topology as a Banach space. On the other hand S is compact when l 2is given its weak topology.

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