Related papers: A linear preserver problem on maps which are tripl…

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner…

Let $e$ and $v$ be minimal tripotents in a JBW$^*$-triple $M$. We introduce the notion of triple transition pseudo-probability from $e$ to $v$ as the complex number $TTP(e,v)= \varphi_v(e),$ where $\varphi_v$ is the unique extreme point of…

Let $\mathcal{A}$ be a prime $\ast$-algebra and $\Phi$ preserves triple $\ast$-Jordan derivation on $\mathcal{A}$, that is, for every $A,B \in \mathcal{A}$, $$\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B\diamond C+A\diamond…

Let $R$ be a ring with identity, $M,N$ right modules over $R$. An additive mapping $\delta$ from $R$ to $R$ is called derivation on ring $R$ if it satisfies the Leibniz condition. If $\delta$ is a derivation on $R$ and $f:M \rightarrow N$…

We prove that every surjective isometry between the unit spheres of two atomic JBW$^*$-triples $E$ and $B$ admits a unit extension to a surjective real linear isometry from $E$ into $B$. This result constitutes a new positive answer to…

We determine the structure of linear maps on complex (real) square matrices sending unitary (orthogonal) matrices to multiples of unitary (orthogonal) matrices. The result is used to determine the linear preservers of matrix pairs…

In this paper, linear $\varepsilon$-orthogonality preserving mappings are studied. We define $\hat{\varepsilon}\left(T\right) $ as the smallest $\varepsilon$ for which $T$ is $\varepsilon$-orthogonality preserving, and then derive an exact…

Let $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear map on normed spaces. We say that $f$ is close-to-regular when $f^{t****s}=f^{s****t}$ and we say that $f$ is completely regular when all natural extensions are equal. In…

We prove that a subspace of a real JBW$^*$-triple is an $M$-summand if and only if it is a weak$^*$-closed triple ideal. As a consequence, $M$-ideals of real JB$^*$-triples correspond to norm-closed triple ideals. As in the setting of…

In this paper, we study triple derivations and triple homomorphisms of perfect Lie superalgebras over a commutative ring $R$. It is proved that, if the base ring contains $\frac{1}{2}$, $L$ is a perfect Lie superalgebra with zero center,…

Let $Alg \mathcal{N}$ be a nest algebra associated with the nest $ \mathcal{N}$ on a (real or complex) Banach space $\X$. Suppose that there exists a non-trivial idempotent $P\in Alg\mathcal{N}$ with range $P(\X) \in \mathcal{N}$ and…

We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms.…

Let $\Theta=(\theta_{j,k})_{3\times 3}$ be a non-degenerate real skew-symmetric $3\times 3$ matrix, where $\theta_{j,k}\in [0,1).$ For any $\varepsilon>0$, we prove that there exists $\delta>0$ satisfying the following: if $v_1,v_2,v_3$ are…

Let $\mathcal{J}_{\field}$ be the Jordan triple system of all $p \times q$ ($p\neq q$; $p,q >1)$ rectangular matrices over a field $\field$ of characteristic 0 with the triple product $\{x,y,z\}= x y^t z+ z y^t x $, where $y^t$ is the…

We introduce the notion of a Jordan triple module and determine the precise conditions under which every derivation from a JB*-triple E into a Banach (Jordan) triple E-module is continuous. In particular, every derivation from a real or…

Inspired by the 2007 work by M.~Misiurewicz and A.~Rodrigues [Double Standard Maps, M. Misiurewicz, A. Rodrigues, Communications in Mathematical Physics], we consider a family of circle maps that are perturbations of the doubling map on the…

Let $M$ and $N$ be arbitrary von Neumann algebras. For any $a$ in $M$ or in $N$, let $\Delta_{\lambda}(a)$ denote the $\lambda$-Aluthge transform of $a$. Suppose that $M$ has no abelian direct summand. We prove that every bijective map…

Let A be an n by d matrix having full rank n. An orthogonal dual A^{\perp} of A is a (d-n) by d matrix of rank (d-n) such that every row of A^{\perp} is orthogonal (under the usual dot product) to every row of A. We define the orthogonal…

For a given $3 \times 3$ real matrix $A$, the eigenvalue complementarity problem relative to the Lorentz cone consists of finding a real number $\lambda$ and a nonzero vector $x \in \mathbb{R}^3$ such that $x^T(A-\lambda I)x=0$ and both $x$…

Let $V$ denote a nonzero finite-dimensional vector space. A tridiagonal pair on $V$ is an ordered pair $A, A^*$ of maps in ${\rm End}(V)$ such that (i) each of $A, A^*$ is diagonalizable; (ii) there exists an ordering $\lbrace V_i…