| Let H and K be infinite separable Hilbert spaces. For given bounded linear operators A∈B(H) and B∈B(K), denote the2x2upper triangular operator matrix on H⊙K of the formThere are three sections in this thesis, and the main content is as follows:In the first section, we have briefly outlined the research of the spectrum of2x2upper triangular operator matrices and the significant of the research. Besides, some related definitions and the main researched problems are introduced.In the second section, the intersection of generalized Weyl spectrum σgw(Mc) are in-vestigated. For given operators A∈B(H) and B∈B(K), we have studied the description of the set∩σgw(Mc) and obtained some related corollary. Moreover, some concrete examples are presented to illustrate the result.In the last section, the union of generalized Weyl spectrum σgw(Mc) are investigated. For given operators A∈B(H) and B∈B(K), the set∪σgw(Mc) is described. Moreover, some concrete examples are constructed to illustrate the result. |
