Abstract
We prove that if { u k } \{ u^k \} is a sequence of holomorphic functions that takes values in an infinite dimensional Hilbert space H \mathcal {H} , there are unitaries { U k } \{ U^k \} on H \mathcal {H} so that U k u k 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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