Vol. 56, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
Invariant subspaces of compact operators on topological vector spaces

Arthur D. Grainger

Vol. 56 (1975), No. 2, 477–493

Let (H,τ) bc a topological vector space and let T be a compact linear operator mapping H into H (i.e., T[V ] is contained in a τcompact set for some τneighborhood V of the zero vector in H). Sufficient conditions are given for (H,τ) so that T has a non-triviaI, closed invariant linear subspace. In particular, it is shown that any complete, metrizable topological vector space with a Schauder basis satisfies the conditions stated in this paper. The proofs and conditions are stated within the framework of nonstandard analysis.

Mathematical Subject Classification 2000
Primary: 47A15
Secondary: 47B05, 02H25
Received: 16 November 1973
Revised: 12 June 1974
Published: 1 February 1975
Arthur D. Grainger