Klaus-Detlef Kürsten

On C*-Like Locally Convex ∗-Algebras

The main purpose of this paper is to define the notion of C*-like locally convex∗-algebras and to study the structure of such ∗-algebras.

On commutatively dominated Op∗-algebras with Fréchet domains

Suppose that the maximal Op∗-algebra L+(D) on a Frechet domain D contains a sequence of strongly commuting essentially self-adjoint operators which is cofinal in the set of all hermitian elements of L+(D). Then each positive linear functional on L+(D) decomposes in a unique way into a sum of an ultraweakly continuous positive linear functional, a uniformly continuous positive linear functional which vanishes on the finite rank operators, and a positive linear functional which vanishes on the dense subspace of the “very continuous” operators. For bounded linear functionals on certain subspaces of the completion L of L+(D), similar results are satisfied. These results are connected with properties of the uniform topology and the associated bornological topology of L.

On Structure of C*-Like Locally Convex *-Algebras

The main purpose of this note is to study the structure of a class of locally convex *-algebras which behave like C*-algebras.

On Continuity Properties of Vertex Operators

Continuity properties of elements Y(v,z) of complex realized vertex operator algebras in the sense of [2] are investigated by constructing a generalized scale (H R,S ) of Hilbert spaces depending on two parameters such that each Y(v,z)may be considered in a natural way as a continuous linear operator between spaces belonging to this scale. As a consequence, products of vertex operators may be realized as factorization products as well as products of operators on a certain partial inner product space.