North British Functional Analysis Seminar

Vladimir Müller (Prague) -- Universal operators and universal spaces
Abstract: Let H be an infinite-dimensional Hilbert space. By a classical result of Caradus, every surjective operator T in B(H) with infinite-dimensional kernel is universal in the following sense: for each operator S on a separable Hilbert space there exist a constant c > 0 and a subspace M in H invariant for T such that the restriction T|M is similar to cS.  We will discuss the connections of universal operators with the dilation theory and generalizations of the Caradus result for n-tuples of operators, both in commutative and non-commutative setting.  Later on we will discuss  the Gurarii space which exhibits many interesting ”universal” properties in the class of Banach spaces.

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Location: Curtis Auditorium in the Herschel Building
Date/Time: 26th October 2012, 15:00 - 17:30

Published: 12th July 2012