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

Jingbo Xia

doi:10.1090/S0002-9939-07-09113-7

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

Jingbo Xia

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Consider Hankel operators H⋊ and Hψ on the unit sphere in C ⁿ.If n = 1, then a necessary condition for H×* Hψ to be compact is lim_|z||l ||H⋊k_z||||Hψ k _z || = 0. We show that when n ≥ 2, this condition is no longer necessary for H⋊* Hψ to be compact.

Original language	English
Pages (from-to)	1375-1384
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-07-09113-7
State	Published - Apr 2008

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title = "On the compactness of the product of hankel operators on the sphere",

abstract = "Consider Hankel operators H⋊ and Hψ on the unit sphere in C n.If n = 1, then a necessary condition for H×* Hψ to be compact is lim|z||l ||H⋊kz||||Hψ k z || = 0. We show that when n ≥ 2, this condition is no longer necessary for H⋊* Hψ to be compact.",

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N2 - Consider Hankel operators H⋊ and Hψ on the unit sphere in C n.If n = 1, then a necessary condition for H×* Hψ to be compact is lim|z||l ||H⋊kz||||Hψ k z || = 0. We show that when n ≥ 2, this condition is no longer necessary for H⋊* Hψ to be compact.

AB - Consider Hankel operators H⋊ and Hψ on the unit sphere in C n.If n = 1, then a necessary condition for H×* Hψ to be compact is lim|z||l ||H⋊kz||||Hψ k z || = 0. We show that when n ≥ 2, this condition is no longer necessary for H⋊* Hψ to be compact.

UR - https://www.scopus.com/pages/publications/77950615859

U2 - 10.1090/S0002-9939-07-09113-7

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

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

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