Maps preserving 2-idempotency of certain products of operators | Zendy

Hossein Khodaiemehr | Zendy; Fereshteh Sady | Zendy

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Maps preserving 2-idempotency of certain products of operators

Author(s) -

Hossein Khodaiemehr,

Fereshteh Sady

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1712909k

Subject(s) - mathematics , idempotence , surjective function , isomorphism (crystallography) , product (mathematics) , pure mathematics , uniqueness , linear operators , scalar (mathematics) , algebra over a field , mathematical analysis , geometry , chemistry , crystallography , crystal structure , bounded function

Let A,B be standard operator algebras on complex Banach spaces X and Y of dimensions at least 3, respectively. In this paper we give the general form of a surjective (not assumed to be linear or unital) map ? : A ? B such that ?2 : M2(C)?A ? M2(C)?B defined by ?2((sij)2x2) = (?(sij))2x2 preserves nonzero idempotency of Jordan product of two operators in both directions. We also consider another specific kinds of products of operators, including usual product, Jordan semi-triple product and Jordan triple product. In either of these cases it turns out that ? is a scalar multiple of either an isomorphism or a conjugate isomorphism.

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