Nevanlinna-Pick spaces with hyponormal multiplication operators

TL;DR

This paper proves that the Hardy space on the unit disk uniquely satisfies the combined properties of the complete Nevanlinna-Pick condition and hyponormal multiplication operators among irreducible reproducing kernel Hilbert spaces.

Contribution

It establishes the Hardy space as the only non-trivial irreducible space with these specific operator-theoretic and kernel properties.

Findings

Hardy space uniquely satisfies the combined properties.

No other irreducible reproducing kernel Hilbert space has these properties.

The result characterizes the Hardy space among such spaces.

Abstract

We show that the Hardy space on the unit disk is the only non-trivial irreducible reproducing kernel Hilbert space which satisfies the complete Nevanlinna-Pick property and hyponormality of all multiplication operators.