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.
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.