A Study of Closure of An Operator

Praveen Sharma

Title:
A Study of Closure of An Operator

Authors:
Praveen Sharma

Cite This Article :

Praveen Sharma "A Study of Closure of An Operator" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1, December 2020, pp.354-356, URL: https://www.ijtsrd.com/papers/ijtsrd37914.pdf

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Abstract :
In this paper first we generalizes the Hilbert-Adjoint of a linear operator and showed that it is always closed for any linear operator with the condition that the domain of the operator is dense. We also proved that "Let J be a closed operator defined in H with dense domain then D(J*) is dense and J** = J . " We also proves Closed graph theorem for complex Hilbert spaces as a corollary of our results.

Keywords :
Separable, Closable, Closure, Operator extension

Publication Details:

Unique Identification Number : IJTSRD37914

Published In : Volume-5 | Issue-1, December 2020

Page Number(s) : 354-356

Publisher Name : IJTSRD | www.ijtsrd.com | E-ISSN 2456-6470

Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0)

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