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A trace formula for Hankel operators

Author(s): Aurelian Gheondea; Raimund J. Ober
Journal: Proc. Amer. Math. Soc. 127 (1999), 2007-2012.
MSC (1991): Primary 47B35; Secondary 47A56, 93B28
Posted: February 26, 1999
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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 $H_G$ with symbol $G$ is of trace-class, then $G$ has continuous extension to the imaginary axis,

\begin{displaymath}G(\infty):=\lim\limits _{r \rightarrow \infty \atop r \in {\Bbb R}} G(r)\end{displaymath}

exists in the trace-class norm, and $\operatorname{tr}(H_G)={1\over 2}\, \operatorname{tr}(G(0)-G(\infty))$.

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Additional Information:

Aurelian Gheondea
Affiliation: Institutul de Matematica al Academiei Romane, C.P. 1-764, 70700 Bucuresti, Romania
Email: gheondea@imar.ro

Raimund J. Ober
Affiliation: Center for Engineering Mathematics EC35, University of Texas at Dallas, Richardson, Texas 75083-0688
Email: ober@utdallas.edu

DOI: 10.1090/S0002-9939-99-04669-9
PII: S 0002-9939(99)04669-9
Received by editor(s): May 29, 1997
Received by editor(s) in revised form: September 10, 1997
Posted: February 26, 1999
Additional Notes: This research was supported in part by NSF grant DMS-9501223.
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1999, American Mathematical Society

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