Weyl type theorem for operator matrices
Volume 186 / 2008
Studia Mathematica 186 (2008), 29-39 MSC: 47A15, 47A53, 47A55. DOI: 10.4064/sm186-1-4
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 $2\times 2$ operator matrices. In this paper, we explore how they survive for $2\times 2$ operator matrices on a Hilbert space.