We prove that two dual operator spaces X and Y are stably isomorphic if and only if there exist completely isometric normal representations φ and ψ of X and Y , respectively, and ternary rings of operators M1,M2 such that φ(X) = [M ∗ 2 ψ(Y )M1] −w ∗ and ψ(Y ) = [M2φ(X)M ∗ 1 ]. We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being ...

We elaborate on the convexity properties of (not necessarily finite) weakly median graphs and their prime constituents in order to establish a number of equations in terms of the weakly median operation. Then the weakly median graphs can be identified with the discrete members of an equational class of ternary algebras satisfying five independent axioms on two to four points. This demonstrates ...

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are deened by a decomposable 3-vector eld. The key point is the proof of a lemma which tells that an n-vector (n 3) is decomposable ii all its contractions with up to n ? 2 covectors are decomposable. In the last years, several authors have studied genera...

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are deened by a decomposable 3-vector eld. The key point is the proof of a lemma which tells that an n-vector (n 3) is decomposable ii all its contractions with up to n ? 2 covectors are decomposable. In the last years, several authors have studied genera...

In this paper we present the groundwork for an It\^o/Malliavin stochastic calculus and Hida's white noise analysis in context of a supersymmentry with Z3-graded algebras. To end establish ternary Fock space corresponding strong algebra distributions its application study processes context.

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

In the present paper, we prove that every local and $2$-local derivation of complex finite-dimensional simple Filippov algebra is a derivation. As corollary have description all derivations semisimple algebras. All ternary Malcev $M_8$ are described. It first example admits pure derivations, i.e. which not

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.