Wandering Montel theorems for Hilbert space valued holomorphic functions

Agler, Jim; McCarthy, John

doi:10.1090/proc/14086

Wandering Montel theorems for Hilbert space valued holomorphic functions
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by Jim Agler and John E. McCarthy PDF

Proc. Amer. Math. Soc. 146 (2018), 4353-4367 Request permission

Abstract:

We prove that if $\{ u^k \}$ is a sequence of holomorphic functions that takes values in an infinite dimensional Hilbert space $\mathcal {H}$, there are unitaries $\{ U^k \}$ on $\mathcal {H}$ so that $U^k u^k$ has a subsequence that converges locally uniformly. We also prove a non-commutative version of this result.

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