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Lipschitz  -summing operators
Author(s):
Jeffrey
D.
Farmer;
William
B.
Johnson
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2989-2995.
MSC (2000):
Primary 46B28, 46T99, 47H99, 47L20
Posted:
April 15, 2009
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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.
References:
-
- 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
 , 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)
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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:
10.1090/S0002-9939-09-09865-7
PII:
S 0002-9939(09)09865-7
Keywords:
$p$-summing operator,
absolutely summing operator.
Received by editor(s):
January 8, 2008
Posted:
April 15, 2009
Additional Notes:
The second author was supported in part by NSF DMS-0503688
Communicated by:
Marius Junge
Copyright of article:
Copyright
2009,
By the authors
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