Concept of s-Numbers in Quaternionic Analysis and Schatten Classes

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-30 DOI:10.1007/s00006-023-01311-w

João Costa

引用次数: 0

Abstract

In this paper we introduce an axiomatic approach to the theory of s-numbers in quaternionic analysis. To this end, Pietsch’s approach to s-number theory is adapted to the quaternionic framework, following the works of Colombo and Sabadini on quaternionic spectral analysis. One of the main results of this paper is the uniqueness of s-numbers over quaternionic Hilbert spaces. Moreover, examples are given in the quaternionic framework together with the introduction of nuclear numbers. A consequence of the presented theory is a basis independent definition of the Schatten classes over quaternionic Hilbert and Banach spaces.

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四元分析中的 s 数概念和沙腾类

本文介绍了四元数分析中 s 数理论的公理化方法。为此，我们根据科伦坡和萨巴迪尼在四元数谱分析方面的研究成果，将皮耶希的 s 数理论方法调整到四元数框架中。本文的主要成果之一是四元希尔伯特空间上 s 数的唯一性。此外，本文还给出了四元数框架下的示例，并引入了核数。所提出的理论的一个结果是四元希尔伯特和巴拿赫空间上的夏顿类的独立于基础的定义。

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

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

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