Vol. 26, No. 1, 1968

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ISSN: 0030-8730
An invariant subspace theorem of J. Feldman

Thomas Alastair Gillespie

Vol. 26 (1968), No. 1, 67–72
Abstract

Theorem. Let t be a quasi-nilpotent bounded linear operator on a complex normed space X of dimension greater than one. Suppose further that there is a sequence {pn(t)} of polynomials in t and a nonzero compact operator s on X such that pn(t) s (in norm) as n →∞. Then t has a proper closed invariant subspace.

Mathematical Subject Classification
Primary: 47.35
Milestones
Received: 18 August 1967
Published: 1 July 1968
Authors
Thomas Alastair Gillespie