Additive Local Multiplications and zero-preserving maps on $C(X)$

从冯·诺伊曼代数到半单Banach代数的加性谱保持映射

Additive spectrum preserving mappings from von Neumann algebras

本文证明了Jafarian的猜想，即从冯·诺伊曼代数到半单巴拿赫代数的加性谱保持映射必然是若尔当同构。

Additive maps preserving idempotency of products or Jordan products of operators

Let H and K be infinite dimensional Hilbert spaces, while B(H) and B(K) denote the algebras of all linear bounded operators on H and K, respectively. We characterize the forms of additive mappings from B(H) into B(K) that preserve the nonzero idempotency of either Jordan products of operators or usual products of operators in both directions.

Orthogonally additive, orthogonality preserving, holomorphic mappings between C*-algebras

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,δ)$ and we assume that $f$ is orthogonality preserving on $A_{sa}\cap U$, orthogonally additive on $U$ and $f(U)$ contains an invertible element in $B$, then there exist a sequence $(h_n)$ in $B^{**}$ and Jordan $^*$-homomorphisms $Θ, \widetildeΘ : M(A) \to B^{**}$ such that $$ f(x) = \sum_{n=1}^\infty h_n \widetildeΘ (a^n)= \sum_{n=1}^\infty Θ (a^n) h_n,$$ uniformly in $a\in U$. W…

Banach代数中的交换保持映射

Commutativity preserving mappings in Banach algebras

研究Banach代数中保持交换性的映射，证明在特定条件下，此类映射可分解为同态与反同态的和，结合中心元和加法映射。

Additive maps preserving the reduced minimum modulus of Banach space operators

Let ${\mathcal B}(X)$ be the algebra of all bounded linear operators on an infinite dimensional complex Banach space $X$. We prove that an additive surjective map $ϕ$ on ${\mathcal B}(X)$ preserves the reduced minimum modulus if and only if either there are bijective isometries $U:X\to X$ and $V:X\to X$ both linear or both conjugate linear such that $ϕ(T)=UTV$ for all $T\in{\mathcal B}(X)$, or $X$ is reflexive and there are bijective isometries $U:X^*\to X$ and $V:X\to X^*$ both linear or both conjugate linear such that $ϕ(T)=UT^*V$ for all $T\in{\mathcal B}(X)$. As immediate consequences of t…

Invariant subspaces of $\mathcal{H}^2(\mathbb{T}^2)$ and $L^2(\mathbb{T}^2)$ preserving compatibility

Operators of multiplication by independent variables on the space of square summable functions over the torus and its Hardy subspace are considered. Invariant subspaces where the operators are compatible are described.