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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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