Location

Crow 206

Start Date

7-18-2016 3:30 PM

End Date

18-7-2016 3:50 PM

Description

The failure of von Neumann's inequality for three commuting contractions has been known since the seventies, thanks to examples of Kaijser-Varopoulos and Crabb-Davie. Nevertheless, this phenomenon is still not well understood. I will talk about a result which shows that von Neumann's inequality holds for a particularly tractable class of commuting contractions, namely multivariable weighted shifts. This provides a positive answer to a question of Lubin and Shields from 1974. As an application, we see that there is no ``nice'' Hilbert function space which is to commuting contractions as the Drury-Arveson space is to commuting row contractions.

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Jul 18th, 3:30 PM Jul 18th, 3:50 PM

von Neumann's inequality for commuting weighted shifts

Crow 206

The failure of von Neumann's inequality for three commuting contractions has been known since the seventies, thanks to examples of Kaijser-Varopoulos and Crabb-Davie. Nevertheless, this phenomenon is still not well understood. I will talk about a result which shows that von Neumann's inequality holds for a particularly tractable class of commuting contractions, namely multivariable weighted shifts. This provides a positive answer to a question of Lubin and Shields from 1974. As an application, we see that there is no ``nice'' Hilbert function space which is to commuting contractions as the Drury-Arveson space is to commuting row contractions.