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Proceedings of the American Mathematical Society
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
Published electronically: April 15, 2009
MathSciNet review: 2506457
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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.


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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: http://dx.doi.org/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
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