Wandering montel theorems for Hilbert space valued holomorphic functions

Jim Agler; John E. McCarthy

doi:10.1090/proc/14086

Wandering montel theorems for Hilbert space valued holomorphic functions

Jim Agler
, John E. McCarthy

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	4353-4367
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	10
DOIs	https://doi.org/10.1090/proc/14086
State	Published - 2018

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title = "Wandering montel theorems for Hilbert space valued holomorphic functions",

abstract = "We prove that if \{uk\} is a sequence of holomorphic functions that takes values in an infinite dimensional Hilbert space H, there are unitaries \{Uk\} on H so that Uk uk has a subsequence that converges locally uniformly. We also prove a non-commutative version of this result.",

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Wandering montel theorems for Hilbert space valued holomorphic functions

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