6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Sourav Pal

A Nagy-Foias program for the C.0 operator tuples associated with the symmetrized polydisc

A commuting tuple of operators (S1,…, Sn-1,P), defined on a Hilbert space H, for which the closed symmetrized polydisc

Γn ={ (1≤ i ≤ n zi,∑1≤i<j ≤ nzizj,…, ∏i=1n zi ):  |zi|≤1, i=1,…,n }

is a spectral set, is called a Γn-contraction. A Γn-contraction (S1,…, Sn-1,P) is said to be C.0 or pure,
if P*n → 0 strongly as n\rightarrow \infty. We show an explicit construction of a Nagy-Foias type dilation and an operator model for the C.0 Γn-contractions. Also we describe a complete unitary invariant for such operator tuples. This is an analogue of the Nagy-Foias complete unitary invariant for a contraction in terms of characteristic function.

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