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A Trace Formula for Hankel Operators

Aurelian Gheondea and Raimund J. Ober
Proceedings of the American Mathematical Society
Vol. 127, No. 7 (Jul., 1999), pp. 2007-2012
Stable URL: http://www.jstor.org/stable/119434
Page Count: 6
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A Trace Formula for Hankel Operators
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Abstract

We show that if G is an operator valued analytic function in the open right half plane such that the Hankel operator HG with symbol G is of trace-class, then G has continuous extension to the imaginary axis, G(∞ ):= $\underset \smallmatrix r\rightarrow \infty \\ r\in {\Bbb R} \endsmallmatrix \to{\lim}$G(r) exists in the trace-class norm, and tr(HG) = 1/2 tr(G(0) - G(∞ )).

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