Lipschitz 
-summing operators
Authors:
Jeffrey D. Farmer and William B. Johnson
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
Published electronically:
April 15, 2009
MathSciNet review:
2506457
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The notion of Lipschitz 
-summing operator is introduced. A nonlinear Pietsch factorization theorem is proved for such operators, and it is shown that a Lipschitz 
-summing operator that is linear is a 
-summing operator in the usual sense.
- 1. K. Ball, Markov chains, Riesz transforms and Lipschitz maps, Geom. Funct. Anal. 2 (1992), no. 2, 137–172. MR 1159828, https://doi.org/10.1007/BF01896971
- 2. 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, https://doi.org/10.1007/s000390050108
- 3. 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
- 4. J. Bourgain, On Lipschitz embedding of finite metric spaces in Hilbert space, Israel J. Math. 52 (1985), no. 1-2, 46–52. MR 815600, https://doi.org/10.1007/BF02776078
- 5. Joe Diestel, Hans Jarchow, and Andrew Tonge, Absolutely summing operators, Cambridge Studies in Advanced Mathematics, vol. 43, Cambridge University Press, Cambridge, 1995. MR 1342297
- 6. 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, https://doi.org/10.1090/S0002-9939-1994-1195718-7
- 7. William B. Johnson, Joram Lindenstrauss, David Preiss, and Gideon Schechtman, Lipschitz quotients from metric trees and from Banach spaces containing 𝑙₁, J. Funct. Anal. 194 (2002), no. 2, 332–346. MR 1934607, https://doi.org/10.1006/jfan.2002.3924
- 8. W. B. Johnson and G. Schechtman, Diamond graphs and super-reflexivity, submitted.
- 9. 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, https://doi.org/10.1215/S0012-7094-06-13415-4
, J. Funct. Anal. 194 (2002), no. 2, 332-346. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B28, 46T99, 47H99, 47L20
Retrieve articles in all journals with MSC (2000): 46B28, 46T99, 47H99, 47L20
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
Email:
johnson@math.tamu.edu
DOI:
https://doi.org/10.1090/S0002-9939-09-09865-7
Keywords:
$p$-summing operator,
absolutely summing operator.
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
Article copyright:
© Copyright 2009
By the authors
