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Zeitschrift für Analysis und ihre Anwendungen


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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.

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Junek Heinz: Maximal Op*-Algebras on DF-Domains. Z. Anal. Anwend. 9 (1990), 403-414. doi: 10.4171/ZAA/411