Lipschitz $p$-summing operators
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- by Jeffrey D. Farmer and William B. Johnson PDF
- Proc. Amer. Math. Soc. 137 (2009), 2989-2995
Abstract:
The notion of Lipschitz $p$-summing operator is introduced. A nonlinear Pietsch factorization theorem is proved for such operators, and it is shown that a Lipschitz $p$-summing operator that is linear is a $p$-summing operator in the usual sense.References
- K. Ball, Markov chains, Riesz transforms and Lipschitz maps, Geom. Funct. Anal. 2 (1992), no. 2, 137–172. MR 1159828, DOI 10.1007/BF01896971
- S. Bates, W. B. Johnson, J. Lindenstrauss, D. Preiss, and G. Schechtman, Affine approximation of Lipschitz functions and nonlinear quotients, Geom. Funct. Anal. 9 (1999), no. 6, 1092–1127. MR 1736929, DOI 10.1007/s000390050108
- Yoav Benyamini and Joram Lindenstrauss, Geometric nonlinear functional analysis. Vol. 1, American Mathematical Society Colloquium Publications, vol. 48, American Mathematical Society, Providence, RI, 2000. MR 1727673, DOI 10.1090/coll/048
- J. Bourgain, On Lipschitz embedding of finite metric spaces in Hilbert space, Israel J. Math. 52 (1985), no. 1-2, 46–52. MR 815600, DOI 10.1007/BF02776078
- Joe Diestel, Hans Jarchow, and Andrew Tonge, Absolutely summing operators, Cambridge Studies in Advanced Mathematics, vol. 43, Cambridge University Press, Cambridge, 1995. MR 1342297, DOI 10.1017/CBO9780511526138
- Jeff D. Farmer, Extreme points of the unit ball of the space of Lipschitz functions, Proc. Amer. Math. Soc. 121 (1994), no. 3, 807–813. MR 1195718, DOI 10.1090/S0002-9939-1994-1195718-7
- William B. Johnson, Joram Lindenstrauss, David Preiss, and Gideon Schechtman, Lipschitz quotients from metric trees and from Banach spaces containing $l_1$, J. Funct. Anal. 194 (2002), no. 2, 332–346. MR 1934607, DOI 10.1006/jfan.2002.3924
- W. B. Johnson and G. Schechtman, Diamond graphs and super-reflexivity, submitted.
- Assaf Naor, Yuval Peres, Oded Schramm, and Scott Sheffield, Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces, Duke Math. J. 134 (2006), no. 1, 165–197. MR 2239346, DOI 10.1215/S0012-7094-06-13415-4
Additional Information
- Jeffrey D. Farmer
- Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
- Email: jdfarmer89@hotmail.com
- William B. Johnson
- Affiliation: Department Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 95220
- Email: johnson@math.tamu.edu
- Received by editor(s): January 8, 2008
- Published electronically: April 15, 2009
- Additional Notes: The second author was supported in part by NSF DMS-0503688
- Communicated by: Marius Junge
- © Copyright 2009 By the authors
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2989-2995
- MSC (2000): Primary 46B28, 46T99, 47H99, 47L20
- DOI: https://doi.org/10.1090/S0002-9939-09-09865-7
- MathSciNet review: 2506457