Weighted holomorphic mappings attaining their norms

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-08-22 DOI:10.1007/s43034-023-00297-7

A. Jiménez-Vargas

引用次数: 0

Abstract

Given an open subset U of \({\mathbb {C}}^n,\) a weight v on U and a complex Banach space F, let \(\mathcal {H}_v(U,F)\) denote the Banach space of all weighted holomorphic mappings \(f:U\rightarrow F,\) under the weighted supremum norm \(\left\| f\right\| _v:=\sup \left\{ v(z)\left\| f(z)\right\| :z\in U\right\} .\) We prove that the set of all mappings \(f\in \mathcal {H}_v(U,F)\) that attain their weighted supremum norms is norm dense in \(\mathcal {H}_v(U,F),\) provided that the closed unit ball of the little weighted holomorphic space \(\mathcal {H}_{v_0}(U,F)\) is compact-open dense in the closed unit ball of \(\mathcal {H}_v(U,F).\) We also prove a similar result for mappings \(f\in \mathcal {H}_v(U,F)\) such that vf has a relatively compact range.

查看原文本刊更多论文

获得范数的加权全纯映射

给定\（｛\mathbb｛C｝｝^n，\）上的权v的开子集U和复Banach空间F，设\（\mathcal{H}_v（U，F）\）表示所有加权全纯映射\（F:U\rightarrow F，\）在加权上确界范数\（\left我们证明了所有映射的集合\（f\in\mathcal{H}_v（U，F）在\（\mathcal{H}_v（U，F），\）给出了小加权全纯空间的闭单位球\（\mathcal{H}_｛v_0｝（U，F）\）在\（\mathcal）的闭单位球中是紧开稠密的{H}_v（U，F）.\）我们还证明了映射\（f\in\mathcal）的类似结果{H}_v（U，F）\）使得vf具有相对紧凑的范围。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.