Motivated by the Q-property of nonsingular M-matrices, Lyapunov and Stein transformations (corresponding to positive stable and Schur stable matrices, respectively) and their products [A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994; M.S. Gowda, Y. Song, Math. Prog. 88 (2000) 575–587; M.S. Gowda, T. Parthasarathy, Linear Algebra Appl. 320 (2...

This paper is devoted to the generalization of construction a Jordan algebra Lie and known theorems on local finite-dimensionality PI-algebras with an algebraic adjoint representation Mal’tsev algebras.

Recently, Bai et al. [Bai Y.Q., Ghami M. El, Roos C., 2004. A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization. SIAM Journal on Optimization, 15(1), 101-128.] provided a unified approach and comprehensive treatment of interior-point methods for linear optimization based on the class of eligible kernel functions. In this paper we generalize t...

Pre-Jordan algebras were introduced recently in analogy with preLie algebras. A pre-Jordan algebra is a vector space A with a bilinear multiplication x · y such that the product x ◦ y = x · y + y · x endows A with the structure of a Jordan algebra, and the left multiplications L·(x) : y 7→ x · y define a representation of this Jordan algebra on A. Equivalently, x ·y satisfies these multilinear ...

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

We consider 3-Jordan algebras, i.e., the nonassociative commutative algebras satisfying (x^3 y)x=x^3(yx). The variety of 3-Jordan algebras contains all Jordan algebras and all pseudo-composition algebras. We prove that a simple 3-Jordan algebra with idempotent is either a Jordan algebra or a pseudo-composition algebra. Disciplines Algebra | Mathematics Comments This article is published as Hent...

Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order symmetries, recursion operators and hierarchies of conservation laws. In this paper the dispersionless limits of these Jordan KdV equations are studied,...