Vol. 21, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 332: 1  2
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 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 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Invariant subspaces of polynomially compact operators on Banach space

Allen Richard Bernstein

Vol. 21 (1967), No. 3, 445–464
Abstract

This paper contains a proof of the following:

Main Theorem. Let T be a bounded linear operator on an infinite-dimensional Banach space B over the complex numbers. Suppose there exists a polynomial p(λ)0 with complex coefficients such that p(T) is compact (completely continuous). Then T leaves invariant at least one closed linear subspace of B other than {0} or B.

Mathematical Subject Classification
Primary: 47.35
Milestones
Received: 25 February 1966
Published: 1 June 1967
Authors
Allen Richard Bernstein