The Livšic function of a homogeneous symmetric operator and the multiplication theorem

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-06-03 DOI:10.1007/s43034-024-00370-9

K. A. Makarov, E. Tsekanovskii

引用次数: 0

Abstract

This paper presents a solution to the Jørgensen–Muhly problem for a homogeneous symmetric operator with deficiency indices (1, 1) that does not admit a homogeneous self-adjoint extension. Based on the Livšic function approach, we characterize the set of all the solutions of the Jørgensen–Muhly problem up to unitary equivalence and describe the complete set of the corresponding unitary invariants.

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同质对称算子的李夫希奇函数和乘法定理

本文提出了一个同质对称算子的 Jørgensen-Muhly 问题的解决方案，该算子具有缺陷指数 (1,1)，不允许同质自关节扩展。基于 Livšic 函数方法，我们描述了 Jørgensen-Muhly 问题所有解的集合，直至单元等价性，并描述了相应单元不变式的完整集合。

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

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.