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# An Infinite Dimensional Vector Space of Universal Functions for $H^\infty$ of the Ball

Published:2007-06-01
Printed: Jun 2007
• Richard Aron
• Pamela Gorkin
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## Abstract

We show that there exists a closed infinite dimensional subspace of $H^\infty(B^n)$ such that every function of norm one is universal for some sequence of automorphisms of $B^n$.
 MSC Classifications: 47B38 - Operators on function spaces (general) 47B33 - Composition operators 46J10 - Banach algebras of continuous functions, function algebras [See also 46E25]