Mennicken, Reinhard and Shkalikov, Andrey A. (1996) Spectral decomposition of symmetric operator matrices. MATHEMATISCHE NACHRICHTEN, 179 (1). pp. 259-273. ISSN 0025-584X, 1522-2616
Full text not available from this repository.Abstract
The authors study symmetric operator matrices L(o) = ((A)(B*) (B)(C)) in the product of Hilbert spaces H = H-1 x H-2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure (L(o)) over bar exists and is a selfadjoint operator in H. With (L(o)) over bar, the closure of the transfer function M(lambda) = C - lambda -B*(A - lambda)B--1 is considered. Under the assumption that there exists a real number beta < inf rho(A) such that M(beta) much less than 0, it follows that beta is an element of rho((L(o)) over bar). Applying a factorization result of A.I. VIROZUB and V.I. MATSAEV [VM] to the holomorphic operator function M(lambda), the spectral subspaces of (L(o)) over bar corresponding to the intervals] - infinity, beta] and [beta, infinity[ and the restrictions of (L(o)) over bar to these subspaces are characterized. Similar results are proved for operator matrices T-o = ((A)(-B*) (B)(C)) which are symmetric in a Krein space.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FACTORIZATION; selfadjoint operator matrices; transfer functions; half range completeness; eigenfunction expansions for PDO |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Nov 2023 07:57 |
| Last Modified: | 15 Nov 2023 07:57 |
| URI: | https://pred.uni-regensburg.de/id/eprint/52105 |
Actions (login required)
 |
View Item |
