论文标题
操作员半群的分类方法
A categorical approach to operator semigroups
论文作者
论文摘要
本文的目的是利用强连续的操作员半群的结构，以制定一个分类框架，在该框架中，可以将新的视角应用于过去的运营商理论结果。特别是，我们调查了Banach代数的逆生产Arens扩展（Trans。Amer。Math。Soc。88：536-548，1958，1958）适用于Batty和Geyer的操作员和操作员（J.运营商理论78（2）：473-500，2017，2017，2017年），在此新框架中，询问和回答问题。我们证明了Arens扩展名在此设置中定义了扩展函数，并且它与适当定义的健忘函数形成了相连。作为该分类框架的副产品，我们还重新审视了Lachowicz和Moszyński的Banach Direct总和（Semigroup Forum论坛93（1）：34-70，2016）。本文可以将其视为对操作员半群，Banach代数和类别理论之间三重接口的简要探索。
The aim of this paper is to exploit the structure of strongly continuous operator semigroups in order to formulate a categorical framework in which a fresh perspective can be applied to past operator theoretic results. In particular, we investigate the inverse-producing Arens extension for Banach algebras (Trans. Amer. Math. Soc. 88:536-548, 1958) adapted for operators and operator semigroups by Batty and Geyer (J. Operator Theory 78(2):473-500, 2017) in this new framework, asking and answering questions using categorical language. We demonstrate that the Arens extension defines an extension functor in this setting and that it forms an adjunction with the suitably defined forgetful functor. As a by-product of this categorical framework, we also revisit the work on Banach direct sums by Lachowicz and Moszyński (Semigroup Forum 93(1):34-70, 2016). This paper can be considered as a brief exploration of the triple interface between operator semigroups, Banach algebras, and category theory.
