A class of operators on Hilbert space
Glenn R. Luecke · Pacific Journal of Mathematics · 1972
If T is an operator (bounded endormorphism) on the complex Hubert space H, then T e & if and only if 11 (Γziy 1 \ | = l/d(s, W(T)) for all z£Q\ W(T), where Cl W(T) is the closure of the numerical range of T and d(z, W(T)) = inf {\z -u\: ue W(T)}.The main results of this paper are: (1) Te & if and only if the boundary of the numerical range of T is a subset of σ(T), the spectrum of T; and (2) & is an arc-wise connected, closed nowhere dense subset of the set of all operators on H (norm topology) when dim H ^ 2. Introduction* If T is an operator (bounded endomorphism) on