# Analízis Tanszék

## 2015.05.06. SELF-ADJOINT DILATIONS IN HILBERT SPACE

Előadó: Nagy Béla (Szeged)

Időpont és hely: 2015. 05. 06., 16 óra, H306

We study self-adjoint dilations of a bounded linear operator $T$ acting in a Hilbert space $H$. It is clear that they cannot be power dilations, and even simple dilations in $H\oplus H$ (in the spirit of Halmos) must be based on a non-classical idea. We study their generalized resolutions of the identity, which are {\it completely bounded} but not necessarily positive operator valued measures. The central variant is distinguished, which shows close connection with the polar decomposition of the operator $T$. It is shown that every operator $T$ in $H$ is the classical compression of an operator in $H\oplus H$ that is similar to a self-adjoint operator.

Tanszékvezető:
Dr. Horváth Miklós
egyetemi tanár
Tel.: 06 1 463 2630

1111 Budapest,
Egry József u. 1.,
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