Vol. 15, No. 2, 1965

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The nilpotent part of a spectral operator. II

Charles Alan McCarthy

Vol. 15 (1965), No. 2, 557–559
Abstract

Let T be a spectral operator on a Banach space, such that its resolvent satisfies a m-th order rate of growth condition. If N be the nilpotent part of T, it is known that Nm = 0 on Hilbert space. We show that Nm = 0 on an Lp space (1 < p < ). Known examples show that Nm need not be zero even on an uniformly convex space.

Mathematical Subject Classification
Primary: 47.40
Milestones
Received: 4 April 1964
Published: 1 June 1965
Authors
Charles Alan McCarthy