Search

Our study is in the set S(H) of all semiclosed operators in a Hilbert space H. We show that the set SSA(H) of all selfadjoint operators is relatively open in the set SSYM(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 Schrödinger operator with a Kato-Rellich potential. [ABSTRACT FROM AUTHOR]

We define a quotient $B/A$ of bounded operators $A$ and $B$ on a Hilbert space $H$ with a kernel condition $\ker A\subset \ker B$ as the mapping $Au\to Bu$, $u\in H$. A quotient $B/A$ is said to be positive symmetric if $A^*B=B^*A\ge 0$. In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient $B/A$. [ABSTRACT FROM AUTHOR]