Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...

C⁎-algebras, group algebras, and the algebra A(X) of approximable operators on a Banach space X having bounded approximation property are known to be zero product determined. In this paper we give quantitative estimate by showing that, for A, there exists constant α with that every continuous bilinear functional φ:A×A→C linear ξ A such thatsup‖a‖=‖b‖=1⁡|φ(a,b)−ξ(ab)|≤αsup‖a‖=‖b‖=1,ab=0⁡|φ(a,b)|...

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

Let $A$ be an algebra over a field $F$ with $(F)\ne 2$. If is generated as by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ arbitrary vector space $F$, the condition that $\Phi(x^2,x)=0 $ all $x\in A$ implies $\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$ $x,y,z\in A$. This applicable to question of whether zero Lie product determined and also used in pro...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...