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Zeitschrift für Analysis und ihre Anwendungen


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Volume 7, Issue 4, 1988, pp. 309–319
DOI: 10.4171/ZAA/308

Published online: 1988-08-31

Spaces of Continuous Sesquilinear Forms Associated with Unbounded Operator Algebras

Konrad Schmüdgen[1]

(1) Universität Leipzig, Germany

Let $\mathcal A$ be a closed *-algebra of unbounded operators on a dense invariant domain $\mathcal D$ of a Hilbert space, and let $\mathcal {L_A} (\mathcal {D, D'})$ be the vector space of all continuous sequilinear forms on $\mathcal D \times \mathcal D$ relative to the graph topology of $\mathcal A$. We generalize some basic results of the von Neumann algebra theory (von Neumann bicommutant theorem, Kaplansky density theorem) to certain linear subspaces of $\mathcal {L_A} (\mathcal {D, D'})$.

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Schmüdgen Konrad: Spaces of Continuous Sesquilinear Forms Associated with Unbounded Operator Algebras. Z. Anal. Anwend. 7 (1988), 309-319. doi: 10.4171/ZAA/308