Remarks on Lipschitz p-summing operators

In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendieck's Theorem is presented. Finally, we prove that if T : X → y H is Lipschitz with X being a pointed metric space and T(0) = 0 such that T # | H* is q-summing (1 ≤ q ≤...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2011-08, Vol.139 (8), p.2891-2898
Main Authors: CHEN, DONGYANG, ZHENG, BENTUO
Format: Article
Language:English
Subjects:
Acceleration of convergence
Adjoints
Banach space
Exact sciences and technology
Factorization
General mathematics
General topology
General, history and biography
Hilbert spaces
Linear transformations
Mathematical extrapolation
Mathematical theorems
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendieck's Theorem is presented. Finally, we prove that if T : X → y H is Lipschitz with X being a pointed metric space and T(0) = 0 such that T # | H* is q-summing (1 ≤ q ≤ ∞), then T is Lipschitz 1-summing.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2011-10720-2