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Additivity of Jordan elementary maps on nest algebras

โœ Scribed by Pengtong Li; Fangyan Lu

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
220 KB
Volume
400
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let A be a standard subalgebra of a nest algebra on a Hilbert space of dimension greater than one and B an arbitrary algebra. A Jordan elementary map of A ร— B is a pair (M, M * ) where M : A โ†’ B and M * : B โ†’ A are two maps satisfying

In this note, it is proved that for a special class of surjective Jordan elementary maps of A ร— B, every member in it is automatically additive. Also, we construct a counterexample which shows that this result is not necessarily true for all surjective Jordan elementary maps.

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