论文标题
满足分离条件的Banach空间的Mazur-Ulam属性
The Mazur-Ulam property for a Banach space which satisfies a separation condition
论文作者
论文摘要
我们研究了Mazur-Ulam物业，研究$ C $ - 富有的空间，郁郁葱葱的空间和$ C $的常规空间。我们表明，统一的代数和具有上限规范的统一代数的真实部分是$ c $ - 富含的空间，因此是郁郁葱葱的空间。我们证明，在局部紧凑的Hausdorff空间上，代数的代数的均匀闭合的亚代数均匀，该空间在无穷大的$ C $ - $ C $ - extremely justremenly justrally justramely justramely justryly justrane jearsive and ntive of cobles afterlienty aftermenty均可分开基础空间的点，并且没有常见的零。在第3节中，我们在Choquet边界，\ Vsilov边界，强边界点上展示了描述。我们还回忆起一个函数空间强烈分开基础空间中的点的定义。我们需要避免由于这些概念的各种名称而出现的混乱。它们有时与作者不同。准备后，我们研究了第4至6节中的Mazur-Ulam特性。我们在具有Mazur-Ulam特性和复杂的Mazur-Ulam特性的Banach空间上表现出足够的状态。在第5节中，我们考虑一个具有分离条件$（*）$（定义5.1）的Banach空间。我们证明，满足$（*）$的真正Banach空间具有Mazur-Ulam Propety（定理6.1），并且满足$（*）$的复杂Banach空间具有复杂的Mazur-Ulam属性（定理6.3）。在前面的部分中应用结果，我们证明了一个极为$ c $的复杂线性子空间具有复杂的Mazur-Ulam属性（推论6.4）。因此，我们证明，在所有复杂值连续功能的所有复杂连续功能的代数的封闭次数上都定义在一个复杂的Hausdorfffer-6. conpectial thement complectermaz5属性上。
We study $C$-rich spaces, lush spaces, and $C$-extremely regular spaces concerning with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform algebra with the supremum norm are $C$-rich spaces, hence lush spaces. We prove that a uniformly closed subalgebra of the algebra of complex-valued continuous functions on a locally compact Hausdorff space which vanish at infinity is $C$-extremely regular provided that it separates the points of the underlying space and has no common zeros. In section 3 we exhibit descriptions on the Choquet bounday, the \vSilov bounday, the strong boundary points. We also recall the definition that a function space strongly separates the points in the underlying space. We need to avoid the confusion which appears because of the variety of names of these concepts; they sometimes differs from authors to authors. After some preparation, we study the Mazur-Ulam property in sections 4 through 6. We exhibit a sufficient condition on a Banach space which has the Mazur-Ulam property and the complex Mazur-Ulam property. In section 5 we consider a Banach space with a separation condition $(*)$ (Definition 5.1). We prove that a real Banach space satisfying $(*)$ has the Mazur-Ulam propety (Theorem 6.1), and a complex Banach space satisfying $(*)$ has the complex Mazur-Ulam property (Theorem 6.3). Applying the results in the previous sections we prove that an extremely $C$-regular complex linear subspace has the complex Mazur-Ulam property (Corollary 6.4) in section 6. As a consequence we prove that any closed subalgebra of the algebra of all complex-valued continuous functions defined on a locally compact Hausdorff space has the complex Mazur-Ulam property (Corollary 6.5).
