On the operator equation AX = XAX

Authors
Holbrook, J Nordren, E Radjavi, H Rosenthal, P
Citation
J. Holbrook et al., On the operator equation AX = XAX, LIN ALG APP, 295(1-3), 1999, pp. 113-116
Citations number
2
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
00243795 → ACNP
Volume
295
Issue
1-3
Year of publication
1999
Pages
113 - 116
Database
ISI
SICI code
0024-3795(19990701)295:1-3<113:OTOEA=>2.0.ZU;2-K
Abstract
It is shown that for an operator A on a Hilbert space every solution X of t he equation AX = XAX is an idempotent precisely when every restriction of A to an invariant subspace has a dense range. (C) 1999 Elsevier Science Inc. All rights reserved.