RT Journal Article
T1 On the derivations of the quadratic Jordan product in the space of rectangular matrices
A1 Isidro Gómez, José María
K1 JB*-triples
K1 Classical Cartan factors
K1 JB*-triple derivations
K1 Banach-Lie groups
AB Let Mn,m be a rectangular finite dimensional Cartan factor, i.e. the space L(Cn, Cm) with 1 ≤n ≤m, and let δ:Mn,m→ Mn,m be a quadratic Jordan derivation of Mn,m, i.e., a map (neither linearity nor continuity of δ is assumed) that satisfies the functional equation δ{ABA}={δ(A)BA}+{Aδ(B)A}+{ABδ(A)}, (A,B ∈ Mn,m), where (A, B, C) →{A B, C} := 1/2 (AB∗C+CB∗A) stands for the Jordan triple product in Mn,m. We prove that then δ automatically is a continuous complex linear map on Mn,m. More precisely we show that δ admits a representation of the form δ(A) =UA +AV, (A ∈ Mn,m), for a suitable pair U, V of square skew symmetric matrices with complex entries U ∈ Mn,n and V ∈ Mm,m.
PB Elsevier
SN 0021-8693
YR 2023
FD 2023
LK http://hdl.handle.net/10347/33223
UL http://hdl.handle.net/10347/33223
LA eng
NO Journal of Algebra Volume 631, 1 October 2023, Pages 911-927
DS Minerva
RD 24 abr 2026