论文标题
双向Banach空间的等距直接限制
Isometric direct limits of bidual Banach spaces
论文作者
论文摘要
$ n $ ther订单的双方班克空间，称为塔式系统及其直接和反向极限的序列被考虑。在统一代数的最新应用中，我们介绍了两个函数：$ \ textrm {dir} $和$ \ textrm {inv} $分配给Banach Space（以及有限的线性运营商）一些新的Banach Space和运营商。特别有趣的是在连续功能的空间上建造的巨大“塔空间”。我们证明$ \ textrm {dir} $的动作保留直接总和分解。该函子还保留了操作员的光谱，它们的弗雷德尔姆斯和紧凑的特性。在上一节中概述了这些函子在表示函数代数措施的支持位置的位置问题。
Sequences of $n$-th order bidual Banach spaces, called tower systems and their direct and inverse limits are considered. Motivated by recent applications in uniform algebras, we introduce two functors: $\textrm{Dir}$ and $\textrm{Inv}$ assigning to Banach spaces (and to bounded linear operators) some new Banach spaces and operators. Of particular interest is the enormous "tower space" built over the space of continuous functions. We prove that the action of $\textrm{Dir}$ preserves direct sum decompositions. This functor preserves also spectra of operators, their Fredholmness and compactness properties. An application of these functors to the problem of location of supports of representing measures for function algebras is outlined in the last section.
