Operator algebra

In functional analysis, an operator algebra is an algebra of continuous  linear operators on a topological vector space (such as a Banach space), which is typically required to be closed in a specified operator topology. In particular, it is a set of operators with both algebraic and topological closure properties. Though operator algebras are studied in this generality in the research literature (for example, algebras of pseudo-differential operators acting on spaces of distributions), the term operator algebra is usually used in reference to algebras of bounded operators on a Banach space or, even more specially in reference to algebras of operators on a Hilbert space.
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