论文标题
关于Fréchet空间中有界近似特性的研讨会
Seminar about the Bounded Approximation Property in Fréchet Spaces
论文作者
论文摘要
该研讨会的目的是在2012年底在政治瓦尔西亚大学提出的，是为了解释有关Fréchet空间有限的近似属性的几个结果。由于Pełczyński，我们提供了一个重要结果的完整详细证明，该证明声称每个具有有界近似属性的可分开的fréchet空间对于以schauder为基础的Fréchet空间的互补子空间都是同构的。我们还解释了沃格特的核弗雷奇空间的示例，而没有有限的近似特性。此示例比Dubinski引起的原始反例更简单。这些例子解决了漫长的格罗迪尼问题。沃格特（Vogt）稍后获得了一个核弗雷奇功能空间的另一个简单示例，而没有边界近似特性。还解释了Fréchet空间的边界近似属性的关系，并且还解释了符合规范的空间，包括杜宾斯基和Vogt引起的几个结果。
The purpose of this seminar, which was presented at the Universitat Politècnica de València in late 2012, is to explain several results concerning the bounded approximation property for Fréchet spaces. We give a full detailed proof of an important result due to Pełczyński that asserts that every separable Fréchet space with the bounded approximation property is isomorphic to a complemented subspace of a Fréchet space with a Schauder basis. We also explain Vogt's example of a nuclear Fréchet space without the bounded approximation property. This example is simpler than the original counterexample due to Dubinski. These examples solved a long standing problem of Grothendieck. Vogt obtained later another simple example of a nuclear Fréchet function space without the bounded approximation property. The relation of the bounded approximation property for Fréchet spaces with a continuous norm and the countably normable spaces, including several results due to Dubinski and Vogt, is also explained.
