Related papers: Nonlinear $*$-Jordan-type derivations on alternati…

Let $\Phi$ be a unital completely positive (UCP) map on the space of operators on some Hilbert space. We assume that $\Phi$ is $\eta$-idempotent, namely, $\|\Phi^2-\Phi\|_{\mathrm{cb}} \le\eta$, and construct an associated…

We study codimension growth of infinite dimensional Lie algebras over a field of characteristic zero. We prove that if a Lie algebra $L$ is an extension of a nilpotent algebra by a finite dimensional semisimple algebra then the PI-exponent…

The main object of study of this paper is the notion of 3-Lie superalgebras with superderivations. We consider a representation $(\Phi,\mathcal{P})$ of a $3$-Lie superalgebra $\mathcal{Q}$ on $\mathcal{P}$ and construct first-order…

Consider any representation $\phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $\hat{S}(g^*)$ of its dual. Consider the tensor product of $\hat{S}(g^*)$ and the exterior algebra $\Lambda(g)$. We…

Let $\cX$ be the unital *-algebra generated by the unilateral shift operator. It is shown that for any nonnegative operator $X\in \cX$ there is an element $Y\in \cX$ such that $X=Y^*Y$.

Let ${\mathcal Q}_n^d$ be the vector space of forms of degree $d\ge 3$ on ${\mathbb C}^n$, with $n\ge 2$. The object of our study is the map $\Phi$, introduced in papers [EI], [AI1], that assigns every nondegenerate form in ${\mathcal…

Let J and J' be Jordan rings. We prove under some conditions that if J contains a nontrivial idempotent, then n-multiplicative maps and n-multiplicative derivations from J to J' are additive maps.

It is known that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. In this paper, a new condition for an analogous…

A map $\Phi$ between matrices is said to be zero product preserving if $$ \Phi(A)\Phi(B) = 0 \quad \text{whenever}\quad AB = 0. $$ In this paper, we give concrete descriptions of an additive/linear zero product preserver $\Phi: {\bf…

Let $R$ be a commutative ring $R$ with $1_R$ and with group of units $R^{\times}$. Let $\Phi = \Phi(t_1,\ldots, t_h) = \sum_{i=1}^h \varphi_it_i$ be an $h$-ary linear form with nonzero coefficients $\varphi_1,\ldots, \varphi_h \in R$. Let…

Let $\g$ be a finite dimensional Lie algebra over a field $k$ of characteristic zero. An element $x$ of $\g$ is said to have an \emph{abstract Jordan-Chevalley decomposition} if there exist unique $s,n\in\g$ such that $x=s+n$, $[s,n]=0$ and…

In this paper we will explain an interesting phenomenon which occurs in general nonassociative algebras. More precisely, we establish that any finite-dimensional commutative nonassociative algebra over a field satisfying an identity always…

We show that it is consistent with ZFC that there is a simple nuclear non-separable C*-algebra which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the…

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a central simple division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain…

We conjecture that a unital C$^*$-algebra is a W$^*$-algebra if and only if each of its maximal abelian self-adjoint subalgebras is a W$^*$-algebra; this is a space-free analogue of a known result due to G.K. Pedersen. Our main result is a…

We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable C*-algebra A is asymptotically tracially in the class of C*-algebras with finite nuclear dimension if and only if A is…

To each irreducible infinite dimensional representation $(\pi,\cH)$ of a $C^*$-algebra $\cA$, we associate a collection of irreducible norm-continuous unitary representations $\pi_{\lambda}^\cA$ of its unitary group $\U(\cA)$, whose…

For a derivation d of a commutative Noetherian complex algebra A, a homeomorphism is established between the prime spectrum of the Ore extension A[z;d] and the Poisson prime spectrum of the polynomial algebra A[z] endowed with the Poisson…

We construct a family of unital non-associative algebras $\{T_\alpha\vert~ 2<\alpha\in\mathbb R\}$ such that $\underline{exp}(T_\alpha)=2$, whereas $\alpha\le\overline{exp}(T_\alpha)\le\alpha+1$. In particular, it follows that ordinary…

Let $\Phi$ be a unital positive linear map and let $A$ be a positive invertible operator. We prove that there exist partial isometries $U$ and $V$ such that \[ |\Phi(f(A))\Phi(A)\Phi(g(A))|\leq U^*\Phi(f(A)Ag(A))U \] and…