Related papers: Quadratic & additive mappings on operator commutin…

We define a symmetry map $\varphi$ on a unital $C^\ast$-algebra $\mathcal A$ to be an $\mathbb{R}$-linear map on $\mathcal A$ that generalizes transformations on matrices like: transpose, adjoint, complex-conjugation, conjugation by a…

We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any…

We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $U_q\widehat{\mathfrak{g}}$ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and…

A (semi)brick over an algebra $A$ is a module $S$ such that the endomorphism ring $\operatorname{\mathsf{End}}_A(S)$ is a (product of) division algebra. For each Dynkin diagram $\Delta$, there is a bijection from the Coxeter group $W$ of…

We study pointwise-generalized-inverses of linear maps between C$^*$-algebras. Let $\Phi$ and $\Psi$ be linear maps between complex Banach algebras $A$ and $B$. We say that $\Psi$ is a pointwise-generalized-inverse of $\Phi$ if…

An abelian self-commutator in a C*-algebra $\mathcal{A}$ is an element $A$ that can be written as $A=X^*X-XX^*$, with $X\in\mathcal{A}$ such that $X^*X$ and $XX^*$ commute. It is shown that, given a finite AW*-factor $\mathcal{A}$, there…

Let $\mathfrak{F}$ be a nonarchimedean local field of residual characteristic $p$, and let $G$ denote the group of $\mathfrak{F}$-points of a connected reductive group over $\mathfrak{F}$. For an open compact subgroup $\mathcal{U}$ of $G$…

For a simple real Jordan algebra $V,$ a family of bi-differential operators from $\mathcal{C}^\infty(V\times V)$ to $\mathcal{C}^\infty(V)$ is constructed. These operators are covariant under the rational action of the conformal group of…

We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with $q=p^a$ elements in a fixed isogeny class in terms of pairs consisting of a fractional $\mathbb Z[\pi,q/\pi]$-ideal and a…

The commutation principle proved by Ram\'irez, Seeger, and Sossa (SIAM J Optim 23:687-694, 2013) in the setting of Euclidean Jordan algebras says that for a Fr\'echet differentiable function $\Theta$ and a spectral function $F$, any local…

Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison's anti-lattice theorem, we show that each of these factors is a disjointness free anti-lattice. We characterise disjointness, bands,…

The contributions in this note begin with a new characterization of (positive) scalar multiples of minimal tripotents in a general JB$^*$-triple $E$, proving that a non-zero element $a\in E$ is a positive scalar multiple of a minimal…

D. Benkovi\v{c} described Jordan homomorphisms of algebras of triangular matrices over a commutative unital ring without additive $2$-torsion. We extend this result to the case of noncommutative rings and remove the assumption of additive…

Let $B(H)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space $H$. For $T \in B(H)$ and $\lambda \in \mathbb{C}$, let $H_{T}(\{\lambda\})$ denotes the local spectral subspace of $T$ associated…

In this paper we characterize $\w$-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that quadratic maps with dendritic Julia sets…

We show that a Jordan algebra of compact quasinilpotent operators which contains a nonzero trace class operator has a common invariant subspace. As a consequence of this result, we obtain that a Jordan algebra of quasinilpotent Schatten…

We consider the unital associative algebra $\mathcal{A}$ with two generators $\mathcal{X}$, $\mathcal{Z}$ obeying the defining relation $[\mathcal{Z},\mathcal{X}]=\mathcal{Z}^2+\Delta$. We construct irreducible tridiagonal representations…

Let $\mathcal{H}$ be a complex Hilbert space, $\mathcal{B(H)}$ be the algebra of all bounded linear operators on $\mathcal{H}$ and $\mathcal{A} \subseteq \mathcal{B(H)}$ be a von Neumann algebra without central summands of type $I_1$. For…

Let $\mathcal{M}$ be a $W^*$-algebra and let $LS(\mathcal{M})$ be the algebra of all locally measurable operators affiliated with $\mathcal{M}$. It is shown that for any self-adjoint element $a\in LS(\mathcal{M})$ there exists a…

We investigate the factorization problem as well as the classifying complements problem in the setting of Jordan algebras. Matched pairs of Jordan algebras and the corresponding bicrossed products are introduced. It is shown that any Jordan…