Some Remarks on the Operator T^*T

Fritz Gesztesy; Konrad Schmüdgen

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arXiv · 1802.05793

Some Remarks on the Operator T^*T

Fritz Gesztesy·Konrad Schmüdgen

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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 $S^2$, where $S$ is a symmetric operator, recovering results due to Yu. Arlinskiĭ and Yu. Kovalev [1], [2].

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BibTeX RIS

Fritz Gesztesy, Konrad Schmüdgen. 2018-03-07. Some Remarks on the Operator T^*T. https://arxiv.org/abs/1802.05793

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