Banach空间上箭图表示的反射函子

The Reflection Functors of Representations of Quivers on Banach Spaces

摘要: 本文的目的是将Hilbert空间上的一些性质推广到Banach空间上.本文首先给出箭图及其Banach表示的定义, 关于收点与发点的反射函子以及共变函子的定义, 利用开映射定理,代数同构等定理定义,说明了两类反射函子可通过共变函子建立一个等式, 然后讨论箭图的Banach 表示之间自同态集与其在反射函子作用下的Banach 表示之间自同态集对应的反射函子映射的代数性质, 证明反射函子映射是个代数同构。

Abstract: The purpose of this paper is to extend some properties of Hilbert spaces to Banach spaces. This paper gave the definitions of the quivers and their Banach representations, the definitions of the reflection functors at the sinks and the sources, and the definitions of contravariant functors. By using the open mapping theorem, algebraic isomorphism and other definition theorems, it is shown that two kinds of reflection functors can establish an equality through covariant functors. It also discussed the algebraic properties of the reflection functor map corresponding to the automorphism sets between the Banach representations of the quivers and their Banach representations under the action of the reflection functors. It proved that the reflection functor map is an algebraic isomorphism.