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- W3046572361 abstract "Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n times n$ 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 many Hilbert spaces of analytic functions, such as the Dirichlet space and the Drury-Arveson space, are not subhomogeneous, and hence one has to test Pick matrices of arbitrarily large matrix size $n$. To treat the Drury-Arveson space, we show that multiplier algebras of certain weighted Dirichlet spaces on the disc embed completely isometrically into the multiplier algebra of the Drury-Arveson space." @default.
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- W3046572361 date "2022-01-01" @default.
- W3046572361 modified "2023-09-25" @default.
- W3046572361 title "Multiplier tests and subhomogeneity of multiplier algebras" @default.
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- W3046572361 doi "https://doi.org/10.4171/dm/883" @default.
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