Vol. 84, No. 2, 1979

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Operators satisfying a G1 condition

Calvin R. Putnam

Vol. 84 (1979), No. 2, 413–426

An operator T on a Hilbert space is said to be G1 if (T z)1= 1dist(z,σ(T)) for zσ(T) and completely G1 if, in addition, T has no normal part. Certain results are obtained concerning the spectra of completely G1 operators and of their real parts. It is shown in particular that there exist completely G1 operators having spectra of zero Hausdorff dimension. Some sparseness conditions on the spectrum are given which assure that a G1 operator has a normal part.

Mathematical Subject Classification 2000
Primary: 47B99
Secondary: 47A10
Received: 23 September 1977
Published: 1 October 1979
Calvin R. Putnam