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

Emmanuel Akweittey, Gabriel Obed Fosu, Ahmed Mubarrack

Abstract


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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References


Krantz Steven G.. A Guide to Functional Analysis. The Mathematical Association of America 2013.

Bowers Adam, Kalton Nigel J.. An Introductory Course in Functional Analysis. Springer New York 2014.

Dugundji James. Topology. Prentice Hall 1988.

Debnath Lokenath. Introduction to Hilbert spaces with applications. Acadamic Press 1998.

Saxe Karen. Beginning Functional Analysis. Springer New York 2001.

Gosman Casper, Perdrick George. First Course in Functional Analysis. Prentice Hall; 1st edition 1965.


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