Multiplier Tests and Subhomogeneity of Multiplier Algebras
Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of n n matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider matrices of bounded size n. We connect this problem to the notion of subhomogeneity of non-selfadjoint operator algebras. Our main results show that multiplier algebras of ma