Arcs defined by one-parameter semigroups of operators in Banach spaces with the Radon-Nikodym property
Let T be an operator on a complex Hilbert space H. Some growth conditions on operator radius of the resolvent of T are studied. Moreover, it is shown that the conjecture, due to V. Istratescu, that for operators T satisfying growth condition (G.) sup i 7* 2 - \(Tx, x)\2\ = R2T, 11-11=1 where /?a is the radius of the smallest circular disk containing the spectrum 0-(T), turns out to be false.
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