Zero product preservers and orthogonality preservers in algebras of unbounded operators

2005/03/14 by Werner Timmermann, Timmermann, Werner
Mathematics · #47L60 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47L60

paper · pdf · doi:10.48550/arxiv.math/0503255

arxiv created 2005/03/14 · arxiv updated 2009/12/01

Abstract

Applying a result of abstract ring theory we get that bijective additive mappings on standard algebras of unbounded operators preserving zero products are multiples of ring isomorphisms. The structure of additive bijective mappings on certain classes of standard algebras of unbounded operators preserving orthogonality in both directions is also investigated. The results are quite similar to those for algebras of bounded operators

Related

• On isomorphisms of standard operator algebras
• One-parameter groups of orthogonality preservers on JB^*-algebras
• Additive maps preserving idempotency of products or Jordan products of operators
• Jordan maps on standard operator algebras
• Maps completely preserving the quadratic operators