GENERALIZED LEFT AND RIGHT WEYL SPECTRA OF UPPER TRIANGULAR OPERATOR MATRICES

In this paper, for given operators A epsilon B(H) and B epsilon B(K), the sets of all C epsilon B(K,H) such that M-C = ((A)(0) (C)(B)) is generalized Weyl and generalized left (right) Weyl, are completely described. Furthermore, the following intersections and unions of the generalized left Weyl spectra boolean OR(C epsilon B(K,H)) sigma(g)(lw) (M-C) and boolean AND(C epsilon B(K,H)) sigma(g)(lw) (M-C) are also described, and necessary and sufficient conditions which two operators A epsilon B(H) and B epsilon B(K) have to satisfy in order for M-C to be a generalized left Weyl operator for each C epsilon B(K; H), are presented.