弱紧JB$^*$-三元组与原子JBW$^*$-三元组之间双正交保持映射的自动连续性

紧C$^*$-代数与冯·诺依曼代数之间双正交保持映射的自动连续性

Automatic continuity of biorthogonality preservers between compact C$^*$-algebras and von Neumann algebras

该研究证明了对偶/紧C$^*$-代数及冯·诺依曼代数间的保双正交线性满射具有自动连续性，推进了算子代数映射性质研究。

One-parameter groups of orthogonality preservers on JB$^*$-algebras

In a first objective we improve our understanding about surjective and bijective bounded linear operators preserving orthogonality from a JB$^*$-algebra $\mathcal{A}$ into a JB$^*$-triple $E$. Among many other conclusions, it is shown that a bounded linear bijection $T: \mathcal{A}\to E$ is orthogonality preserving if, and only if, it is biorthogonality preserving if, and only if, it preserves zero-triple-products in both directions (i.e., $\{a,b,c\}=0 \Leftrightarrow \{T(a),T(b),T(c)\}=0$). In the second main result we establish a complete characterization of all one-parameter groups of ortho…

A linear preserver problem on maps which are triple derivable at orthogonal pairs

A linear mapping $T$ on a JB$^*$-triple is called triple derivable at orthogonal pairs if for every $a,b,c\in E$ with $a\perp b$ we have $$0 = \{T(a), b,c\} + \{a,T(b),c\}+\{a,b,T(c)\}.$$ We prove that for each bounded linear mapping $T$ on a JB$^*$-algebra $A$ the following assertions are equivalent: $(a)$ $T$ is triple derivable at zero; $(b)$ $T$ is triple derivable at orthogonal elements; $(c)$ There exists a Jordan $^*$-derivation $D:A\to A^{**}$, a central element $ξ\in A^{**}_{sa},$ and an anti-symmetric element $η$ in the multiplier algebra of $A$, such that $$ T(a) = D(a) + ξ\circ a +…

通过零化子刻画极小三幂等元及其在截断加性保持子研究中的应用

Characterization of minimal tripotents via annihilators and its application to the study of additive preservers of truncations

本文提出了一般 JB$^*$-triple 中极小 tripotent 标量倍数的内部二次零化子极大性刻画，并以此完整表征了原子 JBW$^*$-triple 间双向保持截断的满射加性映射的代数结构。

Maps preserving triple transition pseudo-probabilities

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 $TTP(e,v)= φ_v(e),$ where $φ_v$ is the unique extreme point of the closed unit ball of $M_*$ at which $v$ attains its norm. In the case of two minimal projections in a von Neumann algebra, this correspond to the usual transition probability. We prove that every bijective transformation $Φ$ preserving triple transition pseudo-probabilities between the lattices of tripotents of two atomic JBW$^*$-triples $M$ and $N$ admits an extensi…

算子交换性的保持子

Preservers of Operator Commutativity

该研究刻画了不含I₁、I₂型中心直和项的JBW*代数上双向保持算子交换性的线性双射的结构，还解决了不含I₁型中心直和项的JBW*代数上结合型对称双线性映射与结合型线性映射的形式刻画问题。