Some Remarks on the Operator T^*T

2018/02/15 by Fritz Gesztesy, Konrad Schmüdgen, Gesztesy, Fritz +1
Computer Science · Mathematics · #47B25 #47B65 #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1802.05793

openalex publication_date 2018/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note deals with the operator T^*T, where T is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebestyén and Zs. Tarcsay [13]: If T^*T and TT^* are self-adjoint, then T is closed. In addition, we describe the Friedrichs extension of S², where S is a symmetric operator, recovering results due to Yu. Arlinskiĭ and Yu. Kovalev [1], [2].

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