The semi-Fredholmness and property (ω) for 2×2 upper triangular operator matrices

Abstract

Let M C = ( A C 0 B ) 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 M C for some invertible C ∈ B ( K , H ) , and using the conclusions obtained, we characterize the equivalent conditions such that M C ∈ ( ω ) for any invertible C ∈ B ( K , H ) .