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.

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

We give a simple proof of a characterization of euclidean space due to Aronszajn and derive a well-known characterization due to Jordan & von Neumann as a corollary. A norm || || on a vector space V is euclidean if there is an inner product 〈 , 〉 on V such that ||v|| = √ 〈v,v〉. Characterizations of euclidean normed spaces abound. Amir [1] surveys some 350 characterizations, starting with a well...

The holonomy-flux *-algebra was recently proposed as an algebra of basic kinematical observables for loop quantum gravity. We show the conventional GNS construction breaks down when the the holonomyflux *-algebra is allowed to be a Jordan algebra of observables. To remedy this, we give a Jordan GNS construction for the holonomy-flux *-algebra that is based on trace. This is accomplished by assu...

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.

If a vertex operator algebra V = ⊕n=0Vn satisfies dimV0 = 1, V1 = 0, then V2 has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set Symd(C) of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, cen...