# Wandering Montel Theorems for Hilbert Space Valued Holomorphic Functions

## TL;DR

This paper extends Montel's theorem to Hilbert space valued holomorphic functions and introduces a non-commutative version using unitaries to ensure convergence.

## Contribution

It provides the first Montel theorem for Hilbert space valued functions and develops a non-commutative analogue employing unitaries.

## Key findings

- Established a Montel theorem for Hilbert space valued holomorphic functions.
- Developed a non-commutative version of the theorem using unitaries.
- Demonstrated convergence properties in the non-commutative setting.

## Abstract

We prove a Montel theorem for Hilbert space valued functions, and a non-commutative version of this theorem, by composing with unitaries to achieve convergence.