SPECTRAL PROPERTIES OF A CLASS OF RATIONAL OPERATOR VALUED FUNCTIONS

摘要

We consider a selfadjoint operator function L of the form L(X) := A — /I rb J3*(C — A)~(-1) B under the assumption that the spectrum of b splits into two parts. In case of the sign + with the pencil L there is associated a selfadjoint operator A in some Hilbert space H D W, in case of the sign -witli L there is associated a selfadjoint Bin a Kre&i space K D H. Spectral properties of these associated operators are crucial for the study of the spec-tral properties of L. Sufficient conditions for the fact that the eigenvectors corresponding to certain parts of the spectrum of L form a Biesz basis in "H are given.