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arXiv · 1507.08418

Adjoint of sums and products of operators in Hilbert spaces

Zoltán Sebestyén·Zsigmond Tarcsay
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Abstract

We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint and essentially selfadjoint operators due to Nelson, Kato, Rellich, and Wüst. Our method involves the range of two-by-two matrices of the form $M_{S,T}=\left(\begin{array}{cc}\!\! I & -T\!\!\\ \!\! S& I\!\!\end{array}\right)$ that makes it possible to treat real and complex Hilbert spaces jointly.

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Zoltán Sebestyén, Zsigmond Tarcsay. 2015-07-30. Adjoint of sums and products of operators in Hilbert spaces. https://arxiv.org/abs/1507.08418

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