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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]
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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

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