希尔伯特$$C^{*}$$模块上的积分算子框架

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2024-02-16 DOI:10.1007/s11565-024-00501-z

Nadia Assila, Hatim Labrigui, Abdeslam Touri, Mohamed Rossafi

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引用次数: 0

摘要

框架理论于 1952 年由达芬（Duffin）和谢弗（Schaefer）作为其非谐波傅里叶级数研究的一部分引入，近几十年来，随着在该领域开展的大量工作，框架理论经历了非常有趣的演变。在本文中，我们为希尔伯特（C^{*}\）模块（{\mathcal {H}}\）上所有可相邻算子的集合引入了一个新概念，即积分算子框架，并给出了与积分算子框架的一些构造相关的一些新性质，还建立了一些新结果。我们还提供了一些说明性的例子，以证明我们的结果是可用的。

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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Integral operator frames on Hilbert $C^{*}$-modules

Introduced by Duffin and Schaefer as a part of their work on nonhamonic Fourier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field. In this work, we introduce a new concept that of integral operator frame for the set of all adjointable operators on a Hilbert $C^{*}$-modules ${\mathcal {H}}$ and we give some new properties relating for some construction of integral operator frame, also we establish some new results. Some illustrative examples are provided to advocate the usability of our results.

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来源期刊

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.