Open Access
Winter 2012 Completely $(q,p)$-mixing maps
Javier Alejandro Chávez-Domínguez
Illinois J. Math. 56(4): 1169-1183 (Winter 2012). DOI: 10.1215/ijm/1399395827


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.


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Javier Alejandro Chávez-Domínguez. "Completely $(q,p)$-mixing maps." Illinois J. Math. 56 (4) 1169 - 1183, Winter 2012.


Published: Winter 2012
First available in Project Euclid: 6 May 2014

zbMATH: 1292.46038
MathSciNet: MR3231478
Digital Object Identifier: 10.1215/ijm/1399395827

Primary: 46L07
Secondary: 46L52 , 47B10 , 47L20 , 47L25

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 4 • Winter 2012
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