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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the compactness of the product of Hankel operators on the sphere

Author: Jingbo Xia
Journal: Proc. Amer. Math. Soc. 136 (2008), 1375-1384
MSC (2000): Primary 47B07, 47B35
Published electronically: November 23, 2007
MathSciNet review: 2367110
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Abstract: Consider Hankel operators $ H_\varphi $ and $ H_\psi $ on the unit sphere in $ {\text{\bf C}}^n$. If $ n = 1$, then a necessary condition for $ H^\ast _\varphi H_\psi $ to be compact is $ \lim _{\vert z\vert\uparrow 1}\Vert H_\varphi k_z\Vert\Vert H_\psi k_z\Vert = 0$. We show that when $ n \geq 2$, this condition is no longer necessary for $ H^\ast _\varphi H_\psi $ to be compact.

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Additional Information

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260

PII: S 0002-9939(07)09113-7
Received by editor(s): November 30, 2006
Received by editor(s) in revised form: February 14, 2007
Published electronically: November 23, 2007
Additional Notes: This work was supported in part by National Science Foundation grant DMS-0456448.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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