A categorical approach to injective envelopes

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-04-23 DOI:10.1007/s43034-024-00350-z

Arianna Cecco

引用次数: 0

Abstract

We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective envelopes. We also compare the purely categorical definition of injectivity with the ‘standard’ operator theoretical definition. An appendix by D. P. Blecher discusses the unitization of an operator space and its injective envelope.

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注入包络的分类方法

我们探讨了算子空间范畴之间的函数、这些函数的一些性质，并建立了这些范畴中的对象及其在这些函数下的图像之间的关系，特别是关于注入性和注入包络的关系。我们还将注入性的纯分类定义与 "标准 "算子理论定义进行了比较。D. P. Blecher 的附录讨论了算子空间的单位化及其注入包络。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.