New York Journal of Mathematics
Volume 28 (2022), 154-174


Michael Hartz

Embedding dimension of the Dirichlet space

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Published: January 18, 2022.
Keywords: Dirichlet space, complete Pick space, Drury-Arveson space, pseudohyperbolic metric.
Subject: Primary: 46E22; Secondary: 30H50.

The classical Dirichlet space is a complete Pick space, hence by a theorem of Agler and McCarthy, there exists an embedding b of the unit disc into a d-dimensional ball such that composition with b realizes the Dirichlet space as a quotient of the Drury-Arveson space. We show that d =∞ is necessary, even if we only demand that composition with b induces a surjective map between the multiplier algebras.


The author was partially supported by a GIF grant.

Author information

Michael Hartz:
Fachrichtung Mathematik
Universität des Saarlandes
66123 Saarbrücken, Germany