Summary
We use modern probabilistic methods to gain a better understanding of what it means that a Banach space fails to be of cotypeq,q>2. In particular, we prove that a Banach space is of cotypeq if and only if the identity map is (q, 1)-summing. (In a previous work, we had shown that this fails forq=2.)
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Oblatum 2-III-1992
Work partially supported by an NSF grant
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Talagrand, M. Cotype and (q, 1)-summing norm in a Banach space. Invent Math 110, 545–556 (1992). https://doi.org/10.1007/BF01231344
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DOI: https://doi.org/10.1007/BF01231344