克雷因变换和半约束线性关系的半约束扩展

IF 0.8 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2023-12-12 DOI:10.1007/s43036-023-00308-3
Josué I. Rios-Cangas
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引用次数: 0

摘要

Krein变换是Cayley变换的实对应物,它给出了正关系和对称收缩之间的一对一对应关系。它的处理与通常的略有不同,导致线性关系的对合。另一方面,半有界线性关系具有具有半有界自伴扩展的闭半有界对称扩展。给出了半有界线性关系的半有界对称扩展的自洽理论。利用Krein变换,给出了拟零关系的正扩展公式。
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The Krein transform and semi-bounded extensions of semi-bounded linear relations

The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and symmetric contractions. It is treated with a slight variation of the usual one, resulting in an involution for linear relations. On the other hand, a semi-bounded linear relation has closed semi-bounded symmetric extensions with semi-bounded selfadjoint extensions. A self-consistent theory of semi-bounded symmetric extensions of semi-bounded linear relations is presented. Using the Krein transform, a formula of positive extensions of quasi-null relations is provided.

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