Szczegóły publikacji
Opis bibliograficzny
On a class of J-self-adjoint operators with empty resolvent set / Sergii KUZHEL, Carsten Trunk // Journal of Mathematical Analysis and Applications ; ISSN 0022-247X. — 2011 — vol. 379 iss. 1, s. 272–289. — Bibliogr. s. 288–289, Abstr. — Publikacja dostępna online od: 2010-12-24
Autorzy (2)
- AGHKużel Sergiusz
- Trunk Carsten
Dane bibliometryczne
| ID BaDAP | 63285 |
|---|---|
| Data dodania do BaDAP | 2012-01-02 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jmaa.2010.12.048 |
| Rok publikacji | 2011 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Mathematical Analysis and Applications |
Abstract
In the present paper we investigate the set ∑J of all J-self-adjoint extensions of an operator S which is symmetric in a Hilbert space H with deficiency indices 〈2,2〉 and which commutes with a non-trivial fundamental symmetry J of a Krein space (H,[.,.]),. SJ=JS. Our aim is to describe different types of J-self-adjoint extensions of S, which, in general, are non-self-adjoint operators in the Hilbert space H. One of our main results is the equivalence between the presence of J-self-adjoint extensions of S with empty resolvent set and the commutation of S with a Clifford algebra Cl2(J,R), where R is an additional fundamental symmetry with JR=-RJ. This enables one to parameterize in terms of Cl2(J,R) the set of all J-self-adjoint extensions of S with stable C-symmetry. Here an extension has stable C-symmetry if it commutes with a fundamental symmetry and, in turn, this fundamental symmetry commutes with S. Such a situation occurs naturally in many applications, here we discuss the case of indefinite Sturm-Liouville operators and the case of a one-dimensional Dirac operator with point interaction.
