Partial *-Algebras of Closed Linear Operators In Hilbert Space

Abstract

Given a dense domain $\mathcal{D}$ of a Hilbert space, we consider the class of all closed operators which, together with their adjoint, have $\mathcal{D}$ in their domain. A partial $\ast$-algebra of operators on $\mathcal{D}$ is a subset of that class, stable under suitable operations of involution, addition and multiplication, the latter when it is defined. We present two types of such objects and study their properties, both algebraic and topological.

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