Quaternionic Hilbert spaces and a von Neumann inequality

Abstract

We show that Drury's proof of the generalisation of the von Neumann inequality to the case of contractive rows of N-tuples of commuting operators still holds in the quaternionic case. The arguments require a seemingly new result on tensor products of quaternionic Hilbert spaces.

Keywords:

• von Neumann inequality
• Drury–Arveson space
• quaternionic Hilbert spaces
• reproducing kernel Hilbert spaces
• tensor products

AMS Subject Classifications:

• Primary 47A60
• Secondary 46A32
• 47B32
• 47S10