REDUCTION OF POSITIVE SELF-ADJOINT EXTENSIONS

被引：0

作者：

Tarcsay, Zsigmond ^{[1
,2
]}

Sebestyen, Zoltan ^{[2
]}

机构：

[1] Corvinus Univ Budapest, Dept Math, IX Fovam Ter 13-15, H-1093 Budapest, Hungary

[2] Eotvos Lorand Univ, Dept Appl Anal & Computat Math, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

来源：

OPUSCULA MATHEMATICA | 2024年 / 44卷 / 03期

关键词：

positive selfadjoint contractive extension; nonnegative selfadjoint extension; Friedrichs and Krein-von Neumann extension; OPERATORS; FACTORIZATION;

D O I：

10.7494/OpMath.2024.44.3.425

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We revise Krein's extension theory of semi-bounded Hermitian operators by reducing the problem to finding all positive and contractive extensions of the "resolvent operator" (I + T)(-1) of T. Our treatment is somewhat simpler and more natural than Krein's original method which was based on the Krein transform (I-T)(I+T)(-1). Apart from being positive and symmetric, we do not impose any further constraints on the operator T: neither its closedness nor the density of its domain is assumed. Moreover, our arguments remain valid in both real or complex Hilbert spaces.

引用

页码：425 / 438

页数：14

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