Maps preserving numerical radius distance on C -algebras
Maps preserving numerical radius distance on C -algebras
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DOI：
10.4064/sm162-2-1
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发表时间：
2004
影响因子：
0.8
通讯作者：
Zhaofang Bai;J. Hou;Zongben Xu
中科院分区：
文献类型：
--
作者：
Zhaofang Bai;J. Hou;Zongben Xu
本文在较弱的条件下刻画了单位C*-代数A和B之间满足w（（A）（B））= w（AB）的满射非线性映射，其中w（A）是A的数值半径，I是A的单位. 1.导论.世纪中期，L. K.华发起了研究几何矩阵。矩阵几何的基本问题是用尽可能少的几何不变量来表征运动群。Hua发现，对于某些域F，特别是真实的域R和复域C，仅“邻接”不变量（当秩（TS）= 1时，T和S相邻）就可以分别表征它们在矩阵空间、对称矩阵空间、反对称矩阵空间和Hermitian矩阵空间上的运动（直到域的自同构）.受矩阵几何的启发，在无限维情形下也可能提出类似的基本问题。问题.尽可能少地找到算子空间A和B或其中的元素可能具有的性质，这些性质足以确定映射的结构：A！B如果具有这些性质作为不变量，即，它保留了这些属性。因此，问题实际上是为算子发展一种类似的“矩阵几何”。对于B（H），其中H是无穷维al
We characterize surjective nonlinear maps between unital C*-algebras A andB that satisfy w( (A) (B)) = w(A B) for all A;B2A under a mild condition that (I) (0) belongs to the center ofB, where w(A) is the numerical radius of A and I is the unit ofA. 1. Introduction. In the middle forties of the twentieth century, L. K. Hua initiated the study of geometry of matrices. The fundamental problem of geometry of matrices is to characterize the group of motions by as few geometric invariants as possible (8). Hua discovered that, for some elds F, especially the real eld R and complex eld C, the \adjacency" invariant (T and S are adjacent if rank(T S) = 1) alone is sucien t to charac- terize the motions (up to automorphisms of the underlying eld) on spaces of matrices, symmetric matrices, skew-symmetric matrices and hermitian matrices, respectively. Motivated by the geometry of matrices, a similar fundamental question may be raised for the innite-dimension al case. Problem. Find as few as possible properties that may be possessed by operator spaces A and B or by elements in them and that are enough to determine the structure of the map :A!B if has these properties as invariants, i.e., if preserves these properties. Thus the problem is indeed to develop an analog of \geometry of ma- trices" for operators. ForB(H), where H is an innite-dimension al