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.)