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Weyl spectra of operator matrices. (English) Zbl 0965.47011

The author studies Fredholm properties of the operator matrix M C =AC0B for operators in Hilbert spaces. Let ω(T) denote the Weyl spectrum of an operator T, i.e., the set of all complex λ such that λ-T is not a Fredholm operator of index zero. The main result of the paper reads as follows:

ω(A)ω(B)=ω(M C )κ, where κ is the union of some holes in ω(M C ) which are contained in ω(A)ω(B).

This implies that the Weyl spectral radius of M C is independent of C.


MSC:
47A53(Semi-)Fredholm operators; index theories
47A55Perturbation theory of linear operators