Atlas: $\gamma$-contractions and the class $C

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22nd Conference in Operator Theory
July 3-8, 2008
West University
Timisoara, Romania

Organizers
Institute of Mathematics of the Romanian Academy and West University in Timisoara

g-contractions and the class C_0·
by
Dan Popovici
Department of Mathematics, West University of Timisoara, Romania

The work of S. Brehmer on the theory of regular unitary dilations has been extended by R.E. Curto - F.-H. Vasilescu and, subsequently, by D. Timotin for the so-called g-contractions. We prove that the number of (Brehmer's) positivity conditions on a commuting multi-operator T necessary and sufficient in order to ensure g-contractivity can be reduced provided that T has C_0· components. We give, in this case, the precise description of the corresponding model of R.E. Curto and F.-H. Vasilescu, respectively D. Timotin. In particular, we obtain that a g-polydisc contraction of class C_0· has a backwards g-multi-shift extension. We finally deduce a new condition on T, equivalent to g-contractivity, improving or extending results by A. Olofsson and by the author.

Date received: May 29, 2008