Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T04:23:44.959Z Has data issue: false hasContentIssue false
  • English
  • Français

ALGEBRAIC ISOMORPHISMS AND FINITE DISTRIBUTIVE SUBSPACE LATTICES

Published online by Cambridge University Press:  01 June 1999

ORESTE PANAIA
ORESTE PANAIA
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6907, Australia, [email protected]
Get access

Abstract

Let [Lscr ]1 and [Lscr ]2 be finite distributive subspace lattices on real or complex Banach spaces. It is shown that every rank-preserving algebraic isomorphism of Alg[Lscr ]1 onto Alg[Lscr ]2 is quasi-spatially induced. If the algebraic isomorphism in question is known only to preserve the rank of rank one operators, then it induces a lattice isomorphism between [Lscr ]1 and [Lscr ]2.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 1033 - 1048
Copyright
The London Mathematical Society 1999

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.)