Illinois Journal of Mathematics

Completely $(q,p)$-mixing maps

Javier Alejandro Chávez-Domínguez

Full-text: Open access

Abstract

Several important results for $p$-summing operators, such as Pietsch’s composition formula and Grothendieck’s theorem, share the following form: there is an operator $T$ such that $S\circ T$ is $p$-summing whenever $S$ is $q$-summing. Such operators were called $(q,p)$-mixing by Pietsch, who studied them systematically. In the operator space setting, G. Pisier’s completely $p$-summing maps correspond to the $p$-summing operators between Banach spaces. A natural modification of the definition yields the notion of completely $(q,p)$-mixing maps, already introduced by K. L. Yew, which is the subject of this paper. Some basic properties of these maps are proved, as well as a couple of characterizations. A generalization of Yew’s operator space version of the Extrapolation theorem is obtained, via an interpolation-style theorem relating different completely $(q,p)$-mixing norms. Finally, some composition theorems for completely $p$-summing maps are proved.

Article information

Source
Illinois J. Math., Volume 56, Number 4 (2012), 1169-1183.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1399395827

Digital Object Identifier
doi:10.1215/ijm/1399395827

Mathematical Reviews number (MathSciNet)
MR3231478

Zentralblatt MATH identifier
1292.46038

Subjects
Primary: 46L07: Operator spaces and completely bounded maps [See also 47L25]
Secondary: 47L25: Operator spaces (= matricially normed spaces) [See also 46L07] 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 46L52: Noncommutative function spaces 47L20: Operator ideals [See also 47B10]

Citation

Chávez-Domínguez, Javier Alejandro. Completely $(q,p)$-mixing maps. Illinois J. Math. 56 (2012), no. 4, 1169--1183. doi:10.1215/ijm/1399395827. https://projecteuclid.org/euclid.ijm/1399395827


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