A Study of Closure of An Operator

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. 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, URL: https://www.ijtsrd.com/papers/ijtsrd37914.pdf Paper URL : https://www.ijtsrd.com/mathemetics/other/37914/a-study-of-closure-of-an-operator/praveen-sharma