Research Article

Generalized Jordan derivable mappings on B ( H )

Published in: Quaestiones Mathematicae
Volume 48 , issue 7 , 2025 , pages: 993–1005

DOI: 10.2989/16073606.2025.2459365

Author(s): Kaijia Luo Institute of Mathematics, Hangzhou Dianzi University, China , Jiankui Li School of Mathematics, East China University of Science and Technology, China , Shanshan Su School of Mathematics, East China University of Science and Technology, China

Keywords: 47B47 , 47L30 , 39B42 , Derivation , generalized Jordan derivable mapping , functional identity

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Abstract

Let be a Hilbert space over the real or complex field and be the algebra of all bounded linear operators on . For arbitrary fixed points C, D, M in , we investigate the structure of linear mappings δ and τ on satisfying one of the following conditions: (i) δ(A)A + Aτ(A) = M for each with A ² = I ; (ii) δ(A)A + Aτ(A) = 0 for each with A ² = 0 whenever is infinite dimensional; (iii) δ(A)B + δ(B)A + Aτ (B) + Bτ(A) = D for all with AB +BA = C. In every case δ, τ are of the form δ(A) = (S +δ(I))A – AT +µ(A) and τ(A) = T A − A(S − τ(I )) − µ(A) for each , where µ is a linear mapping from into and T, S are fixed elements in . In particular, if δ = τ , then there exist such that δ(A) = T′ A – AS′ for each .

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