A trace formula for Hankel operators
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- by Aurelian Gheondea and Raimund J. Ober PDF
- Proc. Amer. Math. Soc. 127 (1999), 2007-2012 Request permission
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, \[ G(\infty ):=\lim \limits _{r \rightarrow \infty \atop r \in \mathcal {R}} G(r)\] exists in the trace-class norm, and $\mathrm {tr}(H_G)={1\over 2} \mathrm {tr}(G(0)-G(\infty ))$.References
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Additional Information
- Aurelian Gheondea
- Affiliation: Center for Engineering Mathematics EC35, University of Texas at Dallas, Richardson, Texas 75083-0688
- 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
- Received by editor(s): May 29, 1997
- Received by editor(s) in revised form: September 10, 1997
- Published electronically: February 26, 1999
- Additional Notes: This research was supported in part by NSF grant DMS-9501223.
- Communicated by: Theodore W. Gamelin
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2007-2012
- MSC (1991): Primary 47B35; Secondary 47A56, 93B28
- DOI: https://doi.org/10.1090/S0002-9939-99-04669-9
- MathSciNet review: 1476131