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...

In this paper we consider the approximate Jordan maps and boundedness of these maps. Also we investigate the stability of approximate Jordan maps and prove some stability properties for approximate Jordan maps. Keywords—Approximate Jordan map; Stability.

Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y , respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is defined by σπ(A) = {z ∈ σ(A) : |z| = maxw∈σ(A) |w|}, where σ(A) denotes the spectrum of A. Assume that Φ : A → B is a map and the range of Φ contains all operators with rank at most two. It is pr...

Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N (X) be the set of nilpotent operators in B(X). Suppose φ : B(X)→ B(X) is a surjective map such that A,B ∈ B(X) satisfy AB ∈ N (X) if and only if φ(A)φ(B) ∈ N (X). If X is infinite dimensional, then there exists a map f : B(X)→ C \ {0} such that one of the following holds: (a) There is a bijective bounded li...

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...

Many authors have studied the local dynamics of holomorphic maps in C around a fixed point; see, for example, [4; 6] for an introduction to this field and known results. Most of the results are obtained under the assumption that the linear part of the map at the fixed point is diagonalizable. There are few results in the nondiagonalizable case. In [8], Coman and Dabija studied a special map wit...

With a detailed investigation of n linear algebraic equations Bx = b, we find that the scaled residual dynamics for y ∈ Sn−1 is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm...