There are several natural generalizations of the notion of C-star-algebra whic allow the linear operators involved to be not necessarily bounded operators. (See Bagarello for a list of literature.) Some variant of these are called *F-star-algebras*, short for *Fréchet-star algebra*.

- F. Bagarello,
*Applications of Topological**-Algebras of Unbounded Operators_ (arXiv:math/9803133)*

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