ACTA issues

## Selfadjoint operators and symmetric operators

Go Hirasawa

Acta Sci. Math. (Szeged) 82:3-4(2016), 529-543
44/2015

 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.)