The Rademacher cotype of operators from $l^ N_ \infty$
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- by S. J. Montgomery-Smith and M. Talagrand PDF
- Proc. Amer. Math. Soc. 112 (1991), 187-194 Request permission
Abstract:
We show that for any operator $T:l_\infty ^N \to Y$, where $Y$ is a Banach space, its cotype 2 constant, ${K^{(2)}}(T)$, is related to its $(2,1)$-summing norm, ${\pi _{2,1}}(T)$, by \[ {K^{(2)}}(T) \leq c\operatorname {log} \operatorname {log} N{\pi _{2,1}}(T).\] Thus, we can show that there is an operator $T:C(K) \to Y$ that has cotype 2, but is not $2$-summing.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 187-194
- MSC: Primary 46B20; Secondary 47B10, 47B37, 60G99
- DOI: https://doi.org/10.1090/S0002-9939-1991-1043416-X
- MathSciNet review: 1043416