Abstract characteristic function

Bhattacharyya, Tirthankar (2012) Abstract characteristic function Complex Analysis and Operator Theory, 6 (1). pp. 91-103. ISSN 1661-8254

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Official URL: http://link.springer.com/article/10.1007%2Fs11785-...

Related URL: http://dx.doi.org/10.1007/s11785-010-0065-6


The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel kS(z,w;)=(1−zw)-1 for |z|, |w| < 1, by means of (1/kS)(T, T*) ≥ 0, we consider an arbitrary open connected domain Ω in Cn, a kernel k on Ω so that 1/k is a polynomial and a tuple T = (T1, T2, . . . , Tn) of commuting bounded operators on a complex separable Hilbert space H such that (1/k)(T, T*) ≥ 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Item Type:Article
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ID Code:99755
Deposited On:27 Nov 2016 12:51
Last Modified:27 Nov 2016 12:51

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