| Abstrakt: |
Let H be a reproducing kernel Hilbert space with a normalized complete Nevanlinna–Pick (CNP) kernel. We prove that if (fn) is a sequence of functions in H with ∑∥fn∥2<∞, then there exists a contractive column multiplier (φn) of H and a cyclic vector F∈H so that φnF=fn for all n. The space of weak products H⊙H is the set of functions of the form h=∑i=1∞figi with fi,gi∈H and ∑i=1∞∥fi∥∥gi∥<∞. Using the above result, in combination with a recent result of Aleman, Hartz, McCarthy, and Richter, we show that for a large class of CNP spaces (including the Drury–Arveson spaces Hd2 and the Dirichlet space in the unit disc) every h∈H⊙H can be factored as a single product h=fg with f,g∈H. [ABSTRACT FROM AUTHOR] |
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