Marcel Schmidt (Jena)

Some counterexamples in operator theory based on Krieger type III dynamical systems

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Types of event
Talk
Venue
Fürstengraben 1, HS 250
07743 Jena
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Speaker
Marius Neubert
Language of the event
English
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No
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This talk takes place in Fürstengraben 1 - HS 250External link

Abstract:

In this talk we show how  the Radon-Nikodym cocycle of Krieger type III dynamical systems can be used to construct two types of operators with an unusual behavior: 

  1. Positivity preserving operators that do not admit optimal functions in the Schur test (an order theoretic description of the operator norm). 
  2. Nonlocal Schrödinger operators which do neither obey the ground state alternative (existence of a generalized ground state v.s. a weighted spectral gap) nor satisfy the Agmon-Allegretto-Piepenbrink principle (a characterization of the bottom of the spectrum).