The nilpotent part of a spectral operator. II

Charles Alan McCarthy

Vol. 15 (1965), No. 2, 557–559

DOI: 10.2140/pjm.1965.15.557

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 N^m = 0 on Hilbert space. We show that N^m = 0 on an L_p space (1 < p < ∞). Known examples show that N^m 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