Abstract
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.
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