The semi-Fredholmness and property (ω) for 2×2 upper triangular operator matrices
Jiong Dong, Xiaohong Cao · Linear and Multilinear Algebra · 2023
Let MC=(AC0B) be a 2×2 upper triangular operator matrix acting on H⊕K, where H and K are complex infinite dimensional separable Hilbert spaces. In this paper, we study the semi-Fredholmness for MC for some invertible C∈B(K,H), and using the conclusions obtained, we characterize the equivalent conditions such that MC∈(ω) for any invertible C∈B(K,H).