Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

   
 
 

 

Lipschitz $ p$-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

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. K. Ball, Markov chains, Riesz transforms and Lipschitz maps, Geom. Funct. Anal. 2 (1992), no. 2, 137-172. MR 1159828 (93b:46025)
  • 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 (2000m:46021)
  • 3. Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis, vol. 1, Amer. Math. Soc. Colloq., Publ., vol. 48, Amer. Math. Soc., Providence, RI, 2000. MR 1727673 (2001b:46001)
  • 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 (87b:46017)
  • 5. J. Diestel, H. Jarchow, and A. Tonge, Absolutely summing operators, Cambridge Studies in Adv. Math., vol. 43, Cambridge Univ. Press, Cambridge, 1995. MR 1342297 (96i:46001)
  • 6. J. 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 (94i:46038)
  • 7. W. B. Johnson, J. Lindenstrauss, D. Preiss, and G. Schechtman, Lipschitz quotients from metric trees and from Banach spaces containing $ l\sb 1$, J. Funct. Anal. 194 (2002), no. 2, 332-346. MR 1934607 (2003h:46023)
  • 8. W. B. Johnson and G. Schechtman, Diamond graphs and super-reflexivity, submitted.
  • 9. A. Naor, Y. Peres, O. Schramm, and S. Sheffield, Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces, Duke Math. J. 134 (2006), no. 1, 165-197. MR 2239346 (2007k:46017)

Similar Articles

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

American Mathematical Society