Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T05:58:17.165Z Has data issue: false hasContentIssue false
  • English
  • Français

INVARIANT SUBSPACES FOR PAIRS OF PROJECTIONS

Published online by Cambridge University Press:  01 April 1998

GRAHAM R. ALLAN  and
JAROSLAV ZEMÁNEK
GRAHAM R. ALLAN
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB. E-mail: G.R.Allan@dpmms.cam.ac.uk
JAROSLAV ZEMÁNEK
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland. E-mail: zemanek@impan.impan.gov.pl
Get access

Abstract

A simple geometrical argument shows that every pair of projections on a finite-dimensional complex vector space has a common invariant subspace of dimension 1 or 2. The idea extends to certain pairs of projections on an infinite-dimensional Hilbert space H. In particular every projection on H has a reducing subspace, although a finite-dimensional one need not exist. In a final section, the results are extended to the existence of hyperinvariant subspaces for pairs of projections.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 449 - 468
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)