Generalized left and right Weyl spectra of upper triangular operator matrices

摘要

In this paper, for given operators $AinB(H)$ and $BinB(K)$, the sets of all $Cin B(K,H)$ such that $M_C=matrix{cc} A&C0&Bendbmatrix$ is generalized Weyl and generalized left (right) Weyl, are completely described. Furthermore, the following intersections and unions of the generalized left Weyl spectra $$ igcup_{CinB(K,H)}sigma^g_{lw}(M_C) ;;; mbox{and} ;;; igcap_{CinB(K,H)}sigma^g_{lw}(M_C) $$ are also described, and necessary and sufficient conditions which two operators $AinB(H)$ and $BinB(K)$ have to satisfy in order for $M_C$ to be a generalized left Weyl operator for each $CinB(K,H)$, are presented.