TOPOLOGIES ON THE OF OPERATIONS ON A HILB

Author (s) : G.MEENAATCHI and M.YAMUNA

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Abstract :
In mathematical field of functional analysis there are several standard topologies which are given to the algebra f(x) of bounded linear operators on a Banach space X. The most commonly used topologies are the norm, strong and weak operator topologies. The weak operator topology is useful for compactness arguments, because the unique ball is compact by the Banach Alaoglu theorem the norm topologies fundamental because it makes B(H) into a anach space but it's too strong. The ultra-weak and ultra-strong topologies are better behaved then the weak and strong operator topologies, but there definitions are more complicated, so they are usually not used unless. We discuss about the weak and weak topologies on a normed linear space. Our aim is to prove the well-known Banach Alaoglu theorem and discuss some of its consequences, in particular characterizations of reflexive space.

Keywords : Functional analysis, mathematical field

Conference Date : 30/08/2019

Pages : 156

Paper ID : 19154