Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (1073 KB) | Metadata | Table of Contents | ZAA summary
Published online: 1990-10-31
Maximal Op*-Algebras on DF-DomainsHeinz Junek (1) Universität Potsdam, Germany
Let $D$ be any dense domain in a Hilbert space and let $\mathcal L^+ (D)$ be the maximaximal Op*-algebra of (possibly unbounded) linear operators. In this paper the uniform topology $\tau_D$ on $\mathcal L^+ (D)$ is investigated for the case where $D$ is a DF-space with respect to the graph topology. As a main result, a characterization of the bounded subsets of $D$ and of the topology $\tau_D$ by strongly bounded selfadjoint operators is given. Especially, each bounded subset of $D$ is contained in some bounded ellipsoid. This is applied to approximate the operators in $\mathcal L^+ (D)$ by bounded ones.
No keywords available for this article.
Junek Heinz: Maximal Op*-Algebras on DF-Domains. Z. Anal. Anwend. 9 (1990), 403-414. doi: 10.4171/ZAA/411