Abstract and Applied Analysis
Volume 2005 (2005), Issue 7, Pages 767-790
Correct selfadjoint and positive extensions of
nondensely defined minimal symmetric operators
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.
be a closed,
minimal symmetric operator from a Hilbert space
with domain not dense in . Let
also be a correct selfadjoint extension of .
The purpose of this paper is (1) to characterize, with the help of
, all the correct selfadjoint extensions of
with domain equal to , (2)
to give the solution of their corresponding problems, (3) to find
sufficient conditions for
to be positive (definite) when
is positive (definite).