On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl2

• Autorzy: Kuzhel S. , Patsyuck O.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Krein spaces; extension theory of symmetric operators; operators with empty resolvent set; J-self-adjoint operators; Clifford algebra Cl2

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 2
• Strony: 297--316
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Kuzhel S.

autor

Patsyuck O.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland,

Bibliografia

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