Partial *-algebras of distributions

Abstract

The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of analytic vectors of a self-adjoint operator is considered, in the framework of the so-called duality method. The multiplication is defined by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain spaces, that are an abstract version of the Bessel potential spaces, are used to factorize the product.