The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (1073 KB) | Metadata | Table of Contents | ZAA summary
Volume 9, Issue 5, 1990, pp. 403–414
DOI: 10.4171/ZAA/411

Published online: 1990-10-31

Maximal Op*-Algebras on DF-Domains

Heinz Junek[1]

(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