Real-linear isometries between function algebras
Real-linear isometries between function algebras
复制标题
函数代数之间的实线性等距
DOI：
10.2478/s11533-011-0044-9
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发表时间：
2011
影响因子：
--
通讯作者：
T. Miura
中科院分区：
文献类型：
--
作者：
T. Miura
设A和B是局部紧Hausdorff空间上的一致闭函数代数，分别具有Choquet边界ChA和ChB.证明了：若T：A → B是满射实线性等距，则存在连续函数κ：ChB → {z ∈ B：|z| = 1}，ChB的一个（可能为空的）闭和开子集K和一个同胚φ：ChB → ChA使得T（f）= K（f <$φ）在K上和$T\left（f \right）= \kappa \overline {fo\phi }$在ChB \ K上对所有f ∈ A。这样的表示适用于函数代数（不一定是一致闭的）之间的满射实线性等距。
Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and $T\left( f \right) = \kappa \overline {fo\phi }$ on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.