[Settfa] Tuesday 20/09, Laurian Suciu

[kubis at math.cas.cz]

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 Tuesday 20th September, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Laurian Suciu, University of Sibiu, Romania
 Title: On Brownian unitary extensions and m-isometric liftings

 Abstract  

 We present several classes of operators on Hilbert spaces having m-isometric liftings or dilations for a positive integer m. The adjoint of an operator which admits such liftings as a backward weighted shift can be seen also as the restriction of a backward shift on a Dirichlet type space of vector-valued analytic functions. These results are applied to concave and convexe operators and also to operators similar to contractions.
 
Also the class of operators admitting Brownian unitary extensions in the context of m-isometries is investigated. The Brownian unitaries here appear as a naturally generalization of the same concept defined by Agler-Stankus in the case of 2-isometries. They show that every 2-isometry has a Brownian unitary extension. In the context of m-isometries with m \ge 3, the class of operators which have such extensions is more restrictive and consists only of expansive m-isometries. These operators can be completely determined and are called sub-Brownian m-isometries, according to S. McCullough's terminology for the case m=3.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .