Remarks on Lipschitz $p$-summing operators
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- by Dongyang Chen and Bentuo Zheng PDF
- Proc. Amer. Math. Soc. 139 (2011), 2891-2898 Request permission
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 $T^\#|_{H^*}$ is $q$-summing $(1\le q<\infty )$, then $T$ is Lipschitz 1-summing.References
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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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2891-2898
- MSC (2010): Primary 46B28, 46T99
- DOI: https://doi.org/10.1090/S0002-9939-2011-10720-2
- MathSciNet review: 2801621