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
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).