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On the Adjoint of Linear Relations in Hilbert Spaces
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2020-02-28 , DOI: 10.1007/s00009-020-1503-y
Adrian Sandovici

Assume that \({\mathfrak {H}}\) and \({\mathfrak {K}}\) are two real or complex Hilbert spaces, A a linear relation from \({\mathfrak {H}}\) to \({\mathfrak {K}}\), and B a linear relation from \({\mathfrak {K}}\) to \({\mathfrak {H}}\), respectively. Necessary and sufficient conditions for B to be equal to the adjoint of A are provided. Several consequences are also presented. More precisely, new characterizations for closed, skew–adjoint, selfadjoint, normal linear relations, and generalized orthogonal projections are obtained.

中文翻译:

希尔伯特空间中线性关系的伴随

假设\({\ mathfrak {H}} \)\({\ mathfrak {K}} \)是两个实数或复数Hilbert空间,从线性关系\({\ mathfrak {H}} \)\({\ mathfrak {K}} \)B分别是从\({\ mathfrak {K}} \)\({\ mathfrak {H}} \)的线性关系。提供了使B等于A的伴随物的充要条件。还提出了一些后果。更精确地,获得了封闭,斜交,自伴,法线线性关系和广义正交投影的新特征。
更新日期:2020-02-28
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