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Towards theory of C-symmetries

Kuzhel S., Sudilovskaya V.

Opuscula Mathematica

2017

Vol. 37, no. 1

65--80

The concept of C-symmetry originally appeared in PT-symmetric quantum mechanics is studied within the Krein spaces framework.

On operators of transition in Krein spaces

Grod A., Kuzhel S., Sudilovskaya V.

Opuscula Mathematica

2011

Vol. 31, no. 1

49-59

The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix L. In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455-486) and show the equivalence between the existence of a strong solution K (//K// < 1) of the Riccati equation and similarity of the J-self-adjoint operator L to a self-adjoint one.