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Bermudo, S.; Marcantognini, S. A. M.; Morán, M. D.

Operators of Hankel type. (English) Zbl 1164.47326

Czech. Math. J. 56, No. 4, 1147-1163 (2006).
Summary: Considering Hankel operators and their symbols, as generalized by V.Pták and P.Vrbová [Acta Sci.Math.52, No.1/2, 117–140 (1988; Zbl 0661.47028)], the present note provides a parametric labeling of all the Hankel symbols of a given Hankel operator \(X\) by means of Schur class functions. The result includes uniqueness criteria and a Schur like formula. As a byproduct, a new proof of the existence of Hankel symbols is obtained. The proof is established by associating to the data of the problem a suitable isometry \(V\) so that there is a bijective correspondence between the symbols of \(X\) and the minimal unitary extensions of \(V\).

Cited in 2 Documents

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A20 Dilations, extensions, compressions of linear operators

Keywords:

Hankel operators; Hankel symbols

Citations:

Zbl 0661.47028
PDFBibTeX XMLCite
\textit{S. Bermudo} et al., Czech. Math. J. 56, No. 4, 1147--1163 (2006; Zbl 1164.47326)
Full Text: DOI EuDML

References:

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