Maps Preserving k -Jordan Products on Operator Algebras

Xiaofei Qi and Miaomiao Wang
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Xiaofei Qi: School of Mathematical Science, Shanxi University, Taiyuan 030006, China
Miaomiao Wang: School of Mathematical Science, Shanxi University, Taiyuan 030006, China

Mathematics, 2020, vol. 8, issue 5, 1-13

Abstract: For any positive integer k , the k -Jordan product of a , b in a ring R is defined by { a , b } k = { { a , b } k − 1 , b } 1 , where { a , b } 0 = a and { a , b } 1 = a b + b a . A map f on R is k -Jordan zero-product preserving if { f ( a ) , f ( b ) } k = 0 whenever { a , b } k = 0 for a , b ∈ R ; it is strong k -Jordan product preserving if { f ( a ) , f ( b ) } k = { a , b } k for all a , b ∈ R . In this paper, strong k -Jordan product preserving nonlinear maps on general rings and k -Jordan zero-product preserving additive maps on standard operator algebras are characterized, generalizing some known results.

Keywords: preservers; jordan products; k -jordan products; standard operator algebras; von neumann algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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