Correct selfadjoint and positive extensions of nondensely defined minimal symmetric operators

I. Parassidis and P. Tsekrekos

Abstract and Applied Analysis, 2005, vol. 2005, 1-24

Abstract:

Let A 0 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 A 0 . The purpose of this paper is (1) to characterize, with the help of A ^ , all the correct selfadjoint extensions B of A 0 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).

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:825134

DOI: 10.1155/AAA.2005.767

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