Jordan τ-Derivations of Locally Matrix Rings

Let R be a prime, locally matrix ring of characteristic not 2 and let Q ms ( R ) be the maximal symmetric ring of quotients of R . Suppose that is a Jordan τ -derivation, where τ is an anti-automorphism of R . Then there exists a  ∈  Q ms ( R ) such that δ ( x ) =  xa  −  aτ ( x ) for all x  ∈  R ....

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Published inAlgebras and representation theory Vol. 16; no. 3; pp. 755 - 763
Main Authors Chuang, Chen-Lian, Fošner, Ajda, Lee, Tsiu-Kwen
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2013
Subjects
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
Prime ring
47B47
47B48
16W25
derivation
Jordan
Banach space
16W10
Locally matrix ring
Jordan homomorphism
Anti-automorphism
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Summary:Let R be a prime, locally matrix ring of characteristic not 2 and let Q ms ( R ) be the maximal symmetric ring of quotients of R . Suppose that is a Jordan τ -derivation, where τ is an anti-automorphism of R . Then there exists a  ∈  Q ms ( R ) such that δ ( x ) =  xa  −  aτ ( x ) for all x  ∈  R . Let X be a Banach space over the field of real or complex numbers and let be the algebra of all bounded linear operators on X . We prove that , which provides the viewpoint of ring theory for some results concerning derivations on the algebra . In particular, all Jordan τ -derivations of are inner if .
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-011-9329-8