Zero product preservers and orthogonality preservers in algebras of unbounded operators

Details Zero product preservers and orthogonality preservers in algebras of unbounded operators Zero product preservers and orthogonality preservers in algebras of unbounded operators

2005-03-14

arxiv.org/abs/math/0503255v1

Mathematics

Operator Algebras

Scientific paper

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

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