Abstract
Our study is in the set {ie529-1}(H) of all semiclosed operators in a Hilbert space H. We show that the set {ie529-2}(H) of all selfadjoint operators is relatively open in the set {ie529-3}(H) of all semiclosed symmetric operators. We calculate the value of a radius of minus-Laplacian -Δ. As a topological approach, we show the selfadjointness of the Schrodinger operator with a Kato.Rellich potential.
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The author would like to thank the referee for his/her careful reading of the manuscript and useful comments about the proof of Theorem 1.1.
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Communicated by L. Kérchy
This work was supported by the Grant-in-Aid for Scientific Research (C), No. 24540160, from the Japan Society for the Promotion of Science.
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Hirasawa, G. Selfadjoint operators and symmetric operators. ActaSci.Math. 82, 529–543 (2016). https://doi.org/10.14232/actasm-015-044-4
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DOI: https://doi.org/10.14232/actasm-015-044-4