Vol. 26, No. 1, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
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