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Set-functions and factorization

Nigel J. Kalton·Stephen J. Montgomery-Smith
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Abstract

If $ϕ$ is a submeasure satisfying an appropriate lower estimate we give a quantitative result on the total mass of a measure $μ$ satisfying $0\leμ\leϕ.$ We give a dual result for supermeasures and then use these results to investigate convexity on non-locally convex quasi-Banach lattices. We then show how to use these results to extend some factorization theorems due to Pisier to the setting of quasi-Banach spaces. We conclude by showing that if $X$ is a quasi-Banach space of cotype two then any operator $T:C(Ω)\to X$ is 2-absolutely summing and factors through a Hilbert space and discussing general factorization theorems for cotype two spaces.

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Nigel J. Kalton, Stephen J. Montgomery-Smith. 1999-12-06. Set-functions and factorization. https://arxiv.org/abs/math/9205206

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