赫米蒂巴纳赫代数上的连续乘法谱函数

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-06-08 DOI:10.1007/s43034-024-00369-2

M. Mabrouk, K. Alahmari, R. Brits

引用次数: 0

摘要

让 \(\mathfrak {A}\) 是一个单元赫米特巴纳赫代数，\(a\in \mathfrak {A}\) 的谱用\(\sigma _\mathfrak {A}(a)\) 表示。我们证明，如果一个连续的乘法函数 \(\phi : \mathfrak {A}\rightarrow \mathbb {C}\) 满足 \(\phi (a)\in \sigma (a)\) for all \(ain \mathfrak {A}\), 那么 \(\phi \) 是线性的，因此是 \(\mathfrak {A}\) 的一个特征。

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Continuous multiplicative spectral functionals on Hermitian Banach algebras

Let \(\mathfrak {A}\) be a unital Hermitian Banach algebra with the spectrum of \(a\in \mathfrak {A}\) denoted by \(\sigma _\mathfrak {A}(a)\). We show that if a continuous and multiplicative function \(\phi : \mathfrak {A}\rightarrow \mathbb {C}\) satisfies \(\phi (a)\in \sigma (a)\) for all \(a\in \mathfrak {A}\), then \(\phi \) is linear and hence a character of \(\mathfrak {A}\).

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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.