On the Merits of Two Different Topologies on the Dual of a Hilbert Space
Abstract
Two topologies of a Hilbert space l 2 is considered in this work. To wit normedvector 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 2∗ is given its topology as a Banach space. On the other hand S is compact when l 2∗ is given its weak topology.
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Published
25-06-2016
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Copyright © The Author(s). This article is published under the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
How to Cite
On the Merits of Two Different Topologies on the Dual of a Hilbert Space. (2016). Asian Journal of Applied Sciences, 4(3). https://ajouronline.com/index.php/AJAS/article/view/3908
