Abstract
In this paper, we consider the well-known transitive algebra problem and reductive algebra problem on vector valued reproducing analytic Hilbert spaces. For an analytic Hilbert space H ( k ) with complete Nevanlinna–Pick kernel k, it is shown that both transitive algebra problem and reductive algebra problem on multiplier invariant subspaces of H ( k ) ⊗ C m have positive answer if the algebras contain all analytic multiplication operators. This extends several known results on the problems.
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