Abstract and Applied Analysis
Volume 2005 (2005), Issue 7, Pages 767-790
doi:10.1155/AAA.2005.767

Correct selfadjoint and positive extensions of nondensely defined minimal symmetric operators

I. Parassidis1 and P. Tsekrekos2

1TEI of Larissa, Larissa 41110, Greece
2Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

Received 13 May 2004

Copyright © 2005 I. Parassidis and P. Tsekrekos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let A0 be a closed, minimal symmetric operator from a Hilbert space ℍ into ℍ with domain not dense in ℍ. Let A^ also be a correct selfadjoint extension of A0. The purpose of this paper is (1) to characterize, with the help of A^, all the correct selfadjoint extensions B of A0 with domain equal to D(A^), (2) to give the solution of their corresponding problems, (3) to find sufficient conditions for B to be positive (definite) when A^ is positive (definite).