Banach Journal of Mathematical Analysis

On the composition ideals of Lipschitz mappings

Khalil Saadi

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1502935412

Digital Object Identifier
doi:10.1215/17358787-2017-0019

Mathematical Reviews number (MathSciNet)
MR3708531

Zentralblatt MATH identifier
06841256

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.bjma/1502935412


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