Abstract
We show that the canonical embeddingC(K) →L Φ(μ) has Gaussian cotypep, where μ is a Radon probability measure onK, and Φ is an Orlicz function equivalent tot p(logt)p/2 for larget.
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References
C. Bennett and K. Rudnick,On Lorentz-Zygmund spaces, Diss. Math.175 (1980), 1–72.
J. Creekmore,Type and cotype in Lorentz L p,q spaces, Indag. Math.43 (1981), 145–152.
G. J. O. Jameson,Summing and Nuclear Norms in Banach Space Theory, London Math. Soc., Student Texts 8, 1987.
J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces I — Sequence Spaces, Springer-Verlag, Berlin, 1977.
B. Maurey,Type et cotype dans les espaces munis de structures locales inconditionelles, Seminaire Maurey-Schwartz 1973–74, Exposés 24–25.
S. J. Montgomery-Smith,The cotype of operators from C(K), Ph.D. thesis, Cambridge University, August 1988.
S. J. Montgomery-Smith,On the cotype of operators from l n∞ , preprint.
M. Talagrand,Regularity of Gaussian processes, Acta Math.159 (1987), 99–149.
M. Talagrand,The canonical injection from C([0, 1])into L 2,1 is not of cotype 2, Contemp. Math.85 (1989), 513–521.
M. Talagrand, Private Communication.
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Montgomery-Smith, S.J. The Gaussian cotype of operators fromC(K). Israel J. Math. 68, 123–128 (1989). https://doi.org/10.1007/BF02764974
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DOI: https://doi.org/10.1007/BF02764974