Annals of Functional Analysis

$(p,\sigma)$-Absolutely Lipschitz operators

D. Achour, P. Rueda, and R. Yahi

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Due to recent advances in the theory of ideals of Lipschitz mappings, we introduce $(p,\sigma)$-absolutely Lipschitz mappings as an interpolating class between Lipschitz mappings and Lipschitz absolutely $p$-summing mappings. Among other results, we prove a factorization theorem that provides a reformulation to the one given by Farmer and Johnson for Lipschitz absolutely $p$-summing mappings.

Article information

Ann. Funct. Anal. Volume 8, Number 1 (2017), 38-50.

Received: 9 March 2016
Accepted: 7 June 2016
First available in Project Euclid: 31 October 2016

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Mathematical Reviews number (MathSciNet)

Primary: 47L20: Operator ideals [See also 47B10]
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 26A16: Lipschitz (Hölder) classes

Lipschitz operators $(p,\sigma)$-absolutely Lipschitz mappings Pietsch factorization theorem


Achour, D.; Rueda, P.; Yahi, R. ( p , σ ) -Absolutely Lipschitz operators. Ann. Funct. Anal. 8 (2017), no. 1, 38--50. doi:10.1215/20088752-3720614.

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