TOPOLOGY VECTOR SPACE

Author (s) : V.RAJESWARI and Dr. P.SOWMIYA

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Abstract :
A topological vector specs (also called a linear topological space) is one of the basic sites inverted in functional analysis. A topological vector space is av space (an algebraic structure) which is also a topological space, the latter there by admiting a notion of continuity More specifically, its topological space has a uniform topological structure, allowing a notion of uniform convergence. The elements of topological typically functions or linear operations acting on apalgeological vector spaces, and the topology is often defined so as to Hilbert spaces and Banach spaces are well-known examples. A metric linear space means a real or complex capture a particolar notion of convergence of sequences of functions vector space together with a metric for which addition and scalar multiplication are continuous. By the Birkhoff-Kakutani theorem, it follws that there is an equivalent metric that is translation-invariant. More strongly a topological vector space is said to be normable if its topology can be induced by a norm. A topological vector space is normal if and only if it is Hausdorff  space and has a convex bounded neighborhood of 0.

Keywords : Topological vector, Hilbert spaces and Banach spaces

Conference Date : 30/08/2019

Pages : 152

Paper ID : 19150