Characteristic function of a pure commuting contractive tuple

Bhattacharyya, T. ; Eschmeier, J. ; Sarkar, J. (2005) Characteristic function of a pure commuting contractive tuple Integral Equations and Operator Theory, 53 (1). pp. 23-32. ISSN 0378-620X

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Official URL: http://link.springer.com/article/10.1007%2Fs00020-...

Related URL: http://dx.doi.org/10.1007/s00020-004-1309-5

Abstract

A theorem of Sz.-Nagy and Foias[9] shows that the characteristic function θT(z)=−T + zDTT∗(1H−zT∗)-1−1DT of a completely non-unitary contraction T is a complete unitary invariant for T. In this note we extend this theorem to the case of a pure commuting contractive tuple using a natural generalization of the characteristic function to an operator-valued analytic function defined on the open unit ball of Cn. This function is related to the curvature invariant introduced by Arveson[3].

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