Operators satisfying aG1condition
Calvin R. Putnam · Pacific Journal of Mathematics · 1979
An operator Ton a Hubert space is said to be G 1 if 11 (T-z)-1 ||=l/dist(s, σ(T)) for z £ σ(T) and completely d if, in addition, T has no normal part.Certain results are obtained concerning the spectra of completely G± operators and of their real parts.It is shown in particular that there exist completely G λ operators having spectra of zero Hausdorff dimension.Some sparseness conditions on the spectrum are given which assure that a G x operator has a normal part.