Related papers: Jordan product commuting maps with $\lambda$-Aluth…

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$, endowed with a rational self-map $\Phi$. Let $\alpha\in G(K)$ and let $\Gamma\subseteq G(K)$ be a finitely generated subgroup. We show that the set…

Let $\mathcal{H}$ be a complex, separable Hilbert space (of finite or infinite dimension), and let $\mathcal{U}(\mathcal{H})$ denote the group of unitary operators on $\mathcal{H}$. A symmetry is, by definition, a unitary operator $J$ with…

In this paper, we prove an analogue of the Jordan canonical form theorem for a class of $n$-normal operators on complex separable Hilbert spaces in terms of von Neumann's reduction theory. This is a continuation of our study of bounded…

Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$…

Let $\Omega \subset {\bf R}^d$ be a bounded open set with Lipschitz boundary $\Gamma$. It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or…

Let $\mathcal{H}$ be a complex finite-dimensional or infinite-dimensional separable Hilbert space, $\mathcal{B(H)}$ and $\mathcal{T(H)}$ be the Banach spaces of all bounded linear operators and of all trace class operators on $\mathcal{H},$…

We establish some Lie--Trotter formulae for unital complex Jordan--Banach algebras, showing that for each couple of elements $a,b$ in a unital complex Jordan--Banach algebra $\mathfrak{A}$ the identities $$ \lim_{n\to \infty}…

Let $\mathbb{K}$ be a field of characteristic different from $2$, and let $M_n(\mathbb{K})$ be the algebra of all $n\times n$ matrices over $\mathbb{K}$. We consider the corresponding special Jordan algebra $\mathcal{A}:=M_n(\mathbb{K})^+$…

In this paper we study multiplication operators on Bergman spaces of high dimensional bounded domains and those von Neumann algebras induced by them via the geometry of domains and function theory of their symbols. In particular, using…

Given a linear map $T$ on a Euclidean Jordan algebra of rank $n$, we consider the set of all nonnegative vectors $q$ in $R^n$ with decreasing components that satisfy the pointwise weak-majorization inequality…

Let $H$ be a complex separable Hilbert space of dimension $\geq 2$, ${\mathcal B}_s(H)$ the space of all self-adjoint operators on $H$. We give a complete classification of non-linear surjective maps on $\mathcal B_s(H)$ preserving…

Let $\ell$ be a commutative ring with involution $*$ containing an element $\lambda$ such that $\lambda+\lambda^*=1$ and let $\operatorname{Alg}^*_\ell$ be the category of $\ell$-algebras equipped with a semilinear involution and involution…

Let $A$ and $B$ be unital rings. An additive map $T:A\to B$ is called a weighted Jordan homomorphism if $c=T(1)$ is an invertible central element and $cT(x^2) = T(x)^2$ for all $x\in A$. We provide assumptions, which are in particular…

Let $\mathcal{H}$ be a linear space equipped with an indefinite inner product $[\cdot, \cdot]$. Denote by $\mathcal{F}_{++}=\{f\in\mathcal{H} \ : \ [f,f]>0\}$ the nonlinear set of positive vectors in $\mathcal{H}$. We demonstrate that the…

Let $E$ and $F$ be two Hilbert $C^*$-modules over $C^*$-algebras $A$ and $B$, respectively. Let $T$ be a surjective linear isometry from $E$ onto $F$ and $\varphi$ a map from $A$ into $B$. We will prove in this paper that if the…

This paper presents some results on simple exceptional Jordan algebra over algebraically closed field $\Phi$ with characteristic not 2. Namely an example of simple decomposition of $H(O_3)$ into the sum of two subalgebras of the type…

This work develops a functional-analytic framework based on the transfinite iteration of a self-adjoint operator. Beginning with a densely defined self-adjoint operator $A$ on a Hilbert space $H$, a spectral-transform functor $\Phi$ is…

Let $T$ be a bounded linear operator on a Hilbert space. Then the Aluthge transform $\Delta T$ and the sequence $(\Delta^nT)$ of Aluthge iterates of $T$ are defined by \begin{align*} \Delta…

Let U be a $\phi $-Johnson amenable Banach algebra in which $\phi$ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that $a.x=\phi(a)x$ for all a in U and x in X or $x.a=\phi(a)x$ for all a in…

The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear maps including derivations, Lie derivations and Jordan derivations. In this paper we introduce the notion of f-biderivations as a natural…