Banach Journal of Mathematical Analysis

On the composition ideals of Lipschitz mappings

Khalil Saadi

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We study some properties of Lipschitz mappings which admit factorization through an operator ideal. Lipschitz cross norms have been established from known tensor norms in order to represent certain classes of Lipschitz mappings. Inspired by the definition of p-summing linear operators, we derive a new class of Lipschitz mappings that is called strictly Lipschitz p-summing.

Article information

Banach J. Math. Anal., Volume 11, Number 4 (2017), 825-840.

Received: 21 June 2016
Accepted: 18 November 2016
First available in Project Euclid: 17 August 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
Secondary: 26A16: Lipschitz (Hölder) classes 47L20: Operator ideals [See also 47B10] 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46M05: Tensor products [See also 46A32, 46B28, 47A80]

Lipschitz operator ideals Lipschitz tensor product (strictly) Lipschitz summing operators factorization of Lipschitz mappings


Saadi, Khalil. On the composition ideals of Lipschitz mappings. Banach J. Math. Anal. 11 (2017), no. 4, 825--840. doi:10.1215/17358787-2017-0019.

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