从几何到可逆性保持映射

有限关联代数的可逆性保持映射

Invertibility preservers of finitary incidence algebras

该研究针对任意偏序集$X$与任意域$K$，通过幂集代数映射与线性映射刻画了有限关联代数$FI(X,K)$的线性单位可逆性保持映射，丰富了关联代数的映射理论。

Linear functions preserving Green's relations over fields

We study linear functions on the space of $n \times n$ matrices over a field which preserve or strongly preserve each of Green's equivalence relations ($\mathcal{L}$, $\mathcal{R}$, $\mathcal{H}$ and $\mathcal{J}$) and the corresponding pre-orders. For each of these relations we are able to completely describe all preservers over an algebraically closed field (or more generally, a field in which every polynomial of degree $n$ has a root), and all strong preservers and bijective preservers over any field. Over a general field, the non-zero $\mathcal{J}$-preservers are all bijective and coincide…

Adjacency preservers on invertible hermitian matrices I

Hua's fundamental theorem of geometry of hermitian matrices characterizes all bijective maps on the space of all hermitian matrices, which preserve adjacency in both directions. In this and subsequent paper we characterize maps on the set of all invertible hermitian matrices over a finite field, which preserve adjacency in one direction. This and author's previous result are used to obtain two new results related to maps that preserve the `speed of light' on finite Minkowski space-time. In this first paper it is shown that maps that preserve adjacency on the set of all invertible hermitian mat…

Fixed product preserving mappings on Banach algebras

In this paper, we describe linear maps between complex Banach algebras that preserve products equal to fixed elements. This generalizes some important special cases where the fixed elements are the zero or identity element. First we show that if such map preserves products equal to a finite-rank operator, then it must also preserve the zero product. In several instances, this is enough to show that a product preserving map must be a scalar multiple of an algebra homomorphism. Second, we explore a more general problem concerning the existence of product preserving maps and the relationship betw…