The joint essential numerical range, compact perturbations, and the Olsen problem
نویسنده
چکیده
Abstract. Let T1, . . . , Tn be bounded linear operators on a complex Hilbert space H. Then there are compact operators K1, . . . , Kn ∈ B(H) such that the closure of the joint numerical range of the n-tuple (T1−K1, . . . , Tn−Kn) equals to the joint essential numerical range of (T1, . . . , Tn). This generalizes the corresponding result for n = 1. We also show that if S ∈ B(H) and n ∈ N then there exists a compact operator K ∈ B(H) such that ‖(S −K)n‖ = ‖S‖e. This generalizes results of C.L. Olsen.
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