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IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-02-12 DOI:10.1002/mana.202400291

Fabio Bagarello, Hiroshi Inoue, Salvatore Triolo

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引用次数: 0

摘要

我们考虑巴拿赫准 * 代数 ( A [ ∥ . ∥ ] , A 0 [ ∥ . ∥ 0 ] ) $({\cal A}[\Vert .\Vert],{\cal A}_0[\Vert .\Vert _0])$，我们称之为元素 a∈A $a\in {\cal A}$ 的特征状态，并推导出它们的一些性质。我们进一步将我们的定义应用于梯形元素族，即服从某些物理换向关系的 A ${\cal A}$ 元素，并讨论了几个结果，包括通过 Gelfand-Naimark-Segal (GNS) 表示的形式的正交性和双正交性。

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Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements

We consider a particular class of sesquilinear forms on a Banach quasi *-algebra $(A [∥ . ∥], A_{0} {[∥ . ∥}_{0}])$ that we call eigenstates of an element $a \in A$ , and we deduce some of their properties. We further apply our definition to a family of ladder elements, that is, elements of $A$ obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via Gelfand–Naimark–Segal (GNS) representation.

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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