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Maps Preserving k -Jordan Products on Operator Algebras

Author

Listed:
  • Xiaofei Qi

    (School of Mathematical Science, Shanxi University, Taiyuan 030006, China
    These authors contributed equally to this work.)

  • Miaomiao Wang

    (School of Mathematical Science, Shanxi University, Taiyuan 030006, China
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Xiaofei Qi & Miaomiao Wang, 2020. "Maps Preserving k -Jordan Products on Operator Algebras," Mathematics, MDPI, vol. 8(5), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:814-:d:359618
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