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Zeitschrift für Analysis und ihre Anwendungen


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Volume 5, Issue 6, 1986, pp. 481–490
DOI: 10.4171/ZAA/217

Published online: 1986-12-31

Topological Realizations of Calkin Algebras on Frechet Domains of Unbounded Operator Algebras

Konrad Schmüdgen[1]

(1) Universität Leipzig, Germany

Let $\mathcal D$ be a dense linear subspace of a separable Hilbert space and let $\mathcal L^+(\mathcal D)$ be the maximal Op*-algebra on $\mathcal D$ endowed with the uniform topology $\tau_{\mathcal D}$. Suppose $\mathcal D$ is a Frechet space with respect to the graph topology of $\mathcal L^+(\mathcal D)$. Let $\mathcal C (\mathcal D)$ denote the two-sided *-ideal of all operators in $\mathcal L^+(\mathcal D)$ which map bounded subsets of $\mathcal D$ into relatively compact subsets. We study the question of when the quotient algebra $\mathcal A (\mathcal D) \colon = \mathcal L^+(\mathcal D) / \mathcal C (\mathcal D)$, endowed with the quotient topology, has a topological realization as an Op*-algebra.

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Schmüdgen Konrad: Topological Realizations of Calkin Algebras on Frechet Domains of Unbounded Operator Algebras. Z. Anal. Anwend. 5 (1986), 481-490. doi: 10.4171/ZAA/217