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Functional Analysis
Universal operators
V. Muller
Tuesday, 20. November 2012 - 10:00
MÚ AV ČR, Žitná 25, konírna
Let $H$ be an infinite-dimensional Hilbert space.
By a classical result of Caradus, every surjective operator $Tin B(H)$ 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 $Msubset H$ 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.
By a classical result of Caradus, every surjective operator $Tin B(H)$ 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 $Msubset H$ 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.