Abstract
A committee space is a Hilbert space of power series, perhaps in several or noncommuting variables, such that $\|z^\alpha\|\|z^\beta\| \geq \|z^{\alpha+\beta}\|.$ Such a space satisfies the true column-row property when ever the map transposing a column multiplier to a row multiplier is contractive. We describe a model for random multipliers and show that such random multipliers satisfy the true column-row property. We also show that the column-row property holds asymptotically for large random Nevanlinna-Pick interpolation problems where the nodes are chosen identically and independently. These results suggest that finding a violation of the true column-row property for the Drury-Arveson space via na\"ive random search is unlikely.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.