TY  - JOUR
ID  - Grod2011
LB  - Grod2011
AU  - Grod, A.
AU  - Kuzhel, S.
AU  - Sudilovskaya, V.
TI  - On operators of transition in Krein spaces
ST  - On operators of transition in Krein spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 1
SP  - 49
EP  - 59
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.1.49
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.1.49
AB  - 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 \(K\) (\(\|K\|\lt 1\)) of the Riccati equation and similarity of the \(J\)-self-adjoint operator \(L\) to a self-adjoint one.
KW  - Krein spaces
KW  - indefinite metrics
KW  - operator of transition
KW  - operator Riccati equation
SN  - 1232-9274
ER  -