所有全函数空间上的托普利兹代数的弗雷德霍姆理论

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-06-07 DOI:10.1002/mana.202300495

M. Jasiczak

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引用次数: 0

摘要

我们证明，当且仅当所有全函数的弗雷谢特空间上的集合托普利兹算子的符号不消失时，它是一个弗雷德霍姆算子。这一结果源于戈伯格和道格拉斯在托普利兹算子的哈代空间理论中得出的经典结果，并与之十分相似。不过，我们也讨论了其中一些微妙的差别。

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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Fredholm theory of the Toeplitz algebra on the space of all entire functions

We prove that an aggregate Toeplitz operator on the Fréchet space of all entire functions is a Fredholm operator if and only if its symbol does not vanish. The result is motivated by and closely resembles the classical result of Gohberg and Douglas from the Hardy space theory of Toeplitz operators. There are however some subtle differences which we also discuss.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index