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A criterion of strong density of operator subalgebras. (English) Zbl 1358.47041
Summary: The purpose of the note is to show the usefulness of a simple criterion of density of a subalgebra \(\mathcal A\subset L(X)\) in the strong operator topology for arbitrary real or complex locally convex vector space \(X\). After proving the criterion we observe its efficiency obtaining short proofs of three important known density theorems plus a new one.
MSC:
47L10 Algebras of operators on Banach spaces and other topological linear spaces
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Full Text: Euclid