Abstract. Our study is in the set ${{\cal S}}(H)$ of all semiclosed operators in a Hilbert space $H$. We show that the set ${{\cal S}}_{sa}(H)$ of all selfadjoint operators is relatively open in the set ${{\cal S}}_{sym}(H)$ of all semiclosed symmetric operators. We calculate the value of a radius of minus-Laplacian $-\Delta $. As a topological approach, we show the selfadjointness of the Schrödinger operator with a Kato--Rellich potential.
DOI: 10.14232/actasm-015-044-4
AMS Subject Classification
(1991): 47A65, 47A05
Keyword(s):
De Branges space,
semiclosed symmetric operators,
selfadjoint operators,
the $q$-metric
Received June 18, 2015, and in revised form January 17, 2016. (Registered under 44/2015.)
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