Fredholm consistency of  upper-triangular operator matrices

Dragana S. Cvetković-Ilić

doi:10.4171/jst/184

JournalsjstVol. 7, No. 4pp. 1023–1038

Fredholm consistency of upper-triangular operator matrices

Dragana S. Cvetković-Ilić
University of Niš, Serbia

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Abstract

In this paper, for given operators $A \in B (H)$ and $B \in B (K)$ , we characterize the set of all $C \in B (K, H)$ such that the operator matrix $M_{C} = [A 0 C B]$ is Fredholm consistent. We completely describe the sets $⋂_{C \in B (K, H)} σ_{FC} (M_{C})$ and $⋃_{C \in B (K, H)} σ_{FC} (M_{C})$ . Also, we prove that $⋂_{C \in B (K, H)} σ_{FC} (M_{C}) = σ_{FC} (M_{0})$ .

Cite this article

Dragana S. Cvetković-Ilić, Fredholm consistency of upper-triangular operator matrices. J. Spectr. Theory 7 (2017), no. 4, pp. 1023–1038

DOI 10.4171/JST/184