Strong (skew) ξ-Lie commutativity preserving maps on algebras

Let [Formula: see text] be a surjective map between some operator algebras such that [Formula: see text] for all [Formula: see text], where [Formula: see text] defined by [Formula: see text] and [Formula: see text] is Jordan product, i.e. [Formula: see text]. In this paper, we determine the concrete form of map [Formula: see text] on some operator algebras. Such operator algebras include standard operator algebras, properly infinite von Neumann algebras and nest algebras. Particularly, if [Formula: see text] is a factor von Neumann algebra that satisfies [Formula: see text] for all [Formula: see text] and idempotents [Formula: see text] then there exists nonzero scalar [Formula: see text] with [Formula: see text] such that [Formula: see text] for all [Formula: see text]

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Maps preserving strong 2-Jordan product on some algebras

Taghavi

Kolivand

2017

Asian-European J. Math.

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Strong (skew) ξ-Lie commutativity preserving maps on algebras

Abstract: Let  be any unital *-algebra over the real or complex field , and let ∈ with ≠ 1.

Cited by 1 publication

References 19 publications

Maps preserving strong 2-Jordan product on some algebras

Maps preserving strong 2-Jordan product on some algebras

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