In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation begin{align*} sum_{k=2}^n sum_{i_1=2}^ksum_{i_2=i_{1}+1}^{k+1}cdotssum_{i_n-k+1=i_{n-k}+1}^n fleft(sum_{i=1,i not=i_{1},cdots ,i_{n-k+1}}^n x_{i}-sum_{r=1}^{n-k+1} x_{i_{r}}right) + fleft(sum_{i=1}^{n}x_{i}right)-2^{n-1} f(x_{1}) =0, end{align*} where ...

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 up...

In this work we introduce generalized projective geometries which are a natural generalization of projective geometries over a field or ring K but also of other important geometries such as Grassmannian, Lagrangian or conformal geometry (see [3]). We also introduce the corresponding generalized polar geometries and associate to such a geometry a symmetric space over K. In the finite-dimensional...

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...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

Let A1,A2 be standard operator algebras on complex Banach spaces X1, X2, respectively. For k ≥ 2, let (i1, . . . , im) be a sequence with terms chosen from {1, . . . , k}, and define the generalized Jordan product T1 ◦ · · · ◦ Tk = Ti1 · · ·Tim + Tim · · ·Ti1 on elements in Ai. This includes the usual Jordan product A1 ◦ A2 = A1A2 + A2A1, and the triple {A1, A2, A3} = A1A2A3 + A3A2A1. Assume th...

We study the “conformal groups” of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where “p-angles” (p ≥ 2) can be defined. We give an oscillator realization of the generalized conformal groups of Jordan algebras and Jordan triple systems. A complete list of the general...

Given the Riemann, or Weyl, a generalized curvature tensor K, symmetric $b_{ij}$ is named `compatible' with if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form special Jordan algebra, i.e. symmetrized product of K-compatible tensors K-compatible.