JORDAN DERIVATIONS AND JORDAN LEFT DERIVATIONS OF BANACH ALGEBRAS

Left Jordan derivations on Banach algebras

In this paper we characterize the left Jordan derivations on Banach algebras. Also, it is shown that every bounded linear map $d:mathcal Ato mathcal M$ from a von Neumann algebra $mathcal A$ into a Banach $mathcal A-$module $mathcal M$ with property that $d(p^2)=2pd(p)$ for every projection $p$ in $mathcal A$ is a left Jordan derivation.

On Jordan left derivations and generalized Jordan left derivations of matrix rings

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

Jordan Homomorphisms and Derivations on Semisimple Banach Algebras

1. Introduction. One may construct a Jordan homomorphism from one (associative) ring into another ring by taking the sum of a homo-morphism and an antihomomorphism of the first ring into two ideals in the second ring with null intersection [6]. A number of authors have considered conditions on the rings that imply that every Jordan homomorphism, or isomorphism, is of this form [6], [3], [7], [1...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

Approximate Quaternary Jordan Derivations on Banach Quaternary Algebras

We show that a quaternary Jordan derivation on a quaternary Banach algebra associated with the equation f( x+ y + z 4 ) + f( 3x− y − 4z 4 ) + f( 4x+ 3z 4 ) = 2f(x) . is satisfied in generalized Hyers–Ulam stability.