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Browder spectra for upper triangular operator matrices. (English) Zbl 1139.47006

Summary: When AB(H) and BB(K) are given, we denote by M C an operator of the form M C =AC0B acting on the infinite-dimensional separable Hilbert space HK. In this paper, we prove that

CB(K,H) σ b (M C )=σ ab (A)σ ab (B * ){λ:n(A-λI)+n(B-λI)d(A-λI)+d(B-λI)},

where σ b (T), σ ab (T), n(T) and T * denote the Browder spectrum, Browder essential approximate point spectrum, nullity, deficiency and conjugate of T, respectively. Some related results are obtained.

47A10Spectrum and resolvent of linear operators
47A53(Semi-)Fredholm operators; index theories
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