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

 

Remarks on Lipschitz $ p$-summing operators


Authors: Dongyang Chen and Bentuo Zheng
Journal: Proc. Amer. Math. Soc. 139 (2011), 2891-2898
MSC (2010): Primary 46B28, 46T99
Published electronically: January 13, 2011
MathSciNet review: 2801621
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Abstract: In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendieck's Theorem is presented. Finally, we prove that if $ T:X\to H$ is Lipschitz with $ X$ being a pointed metric space and $ T(0)=0$ such that $ T^\char93 \vert _{H^*}$ is $ q$-summing $ (1\le q<\infty)$, then $ T$ is Lipschitz 1-summing.


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Additional Information

Dongyang Chen
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
Email: cdy@xmu.edu.cn

Bentuo Zheng
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152-3240
Email: bzheng@memphis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10720-2
PII: S 0002-9939(2011)10720-2
Received by editor(s): January 31, 2010
Received by editor(s) in revised form: July 31, 2010
Published electronically: January 13, 2011
Additional Notes: The first author’s research was supported in part by the National Natural Science Foundation of China (Grants No. 10526034, 10701063).
The second author’s research was supported in part by NSF grant DMS-0800061.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.