- Tytuł:
- On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl2
- Autorzy:
-
Kuzhel, S.
Patsyuck, O. - Powiązania:
- https://bibliotekanauki.pl/articles/256050.pdf
- Data publikacji:
- 2012
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Krein spaces
extension theory of symmetric operators
operators with empty resolvent set
J-self-adjoint operators
Clifford algebra Cl2 - Opis:
- Let J and R be anti-commuting fundamental symmetries in a Hilbert space ℘. The operators J and R can be interpreted as basis (generating) elements of the complex Clifford algebra Cl2(J,R) := span{I, J;R, iJR}. An arbitrary non-trivial fundamental symmetry from Cl2(J,R) is determined by the formula [formula]. Let S be a symmetric operator that commutes with Cl2(J,R). The purpose of this paper is to study the sets [formula] of self-adjoint extensions of S in Krein spaces generated by fundamental symmetries [formula]. We show that the sets [formula] and [formula] are unitarily equivalent for different [formula] and describe in detail the structure of operators [formula] with empty resolvent set.
- Źródło:
-
Opuscula Mathematica; 2012, 32, 2; 297-316
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł