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Using topological uniform descent, we give necessary and sufficient conditions for Browder's theorem and Weyl's theorem to hold for an operator A. The two theorems are liable to fail for 2 × 2 operator matrices. In this paper, we explore how they survive for 2 × 2 operator matrices on a Hilbert space.
Xiaohong Cao. "Weyl type theorem for operator matrices." Studia Mathematica 186.1 (2008): 29-39. <http://eudml.org/doc/284938>.
@article{XiaohongCao2008, abstract = {Using topological uniform descent, we give necessary and sufficient conditions for Browder's theorem and Weyl's theorem to hold for an operator A. The two theorems are liable to fail for 2 × 2 operator matrices. In this paper, we explore how they survive for 2 × 2 operator matrices on a Hilbert space.}, author = {Xiaohong Cao}, journal = {Studia Mathematica}, keywords = {Weyl's theorem; Browder's theorem; topological uniform decent}, language = {eng}, number = {1}, pages = {29-39}, title = {Weyl type theorem for operator matrices}, url = {http://eudml.org/doc/284938}, volume = {186}, year = {2008}, }
TY - JOUR AU - Xiaohong Cao TI - Weyl type theorem for operator matrices JO - Studia Mathematica PY - 2008 VL - 186 IS - 1 SP - 29 EP - 39 AB - Using topological uniform descent, we give necessary and sufficient conditions for Browder's theorem and Weyl's theorem to hold for an operator A. The two theorems are liable to fail for 2 × 2 operator matrices. In this paper, we explore how they survive for 2 × 2 operator matrices on a Hilbert space. LA - eng KW - Weyl's theorem; Browder's theorem; topological uniform decent UR - http://eudml.org/doc/284938 ER -