[Settfa] Tuesday 30/05, Vladimir Muller

[kubis at math.cas.cz]

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 Tuesday 30th May, 10:00am 
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 Speaker:Vladimir Muller, IM CAS
 Title: Circles in the spectrum and numerical ranges

 Abstract  
We prove that a bounded linear Hilbert space operator has the unit circle
in its spectrum if and only if it admits an
orbit satisfying certain orthogonality and almost-orthogonality relations.
As consequences, we derive in particular wide generalizations of Arveson’s
theorem as well as show that the weak convergence of operator
powers implies the uniform convergence of their compressions on an
infinite-dimensional subspace. The unit circle in the spectrum implies also that the operator has interesting universality properties - it contains all strict contractions as its compressions.

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