Inclusions and coincidences for multiple summing multilinear mappings

Botelho, G.; Braunss, H.-A.; Junek, H.; Pellegrino, D.

doi:10.1090/S0002-9939-08-09691-3

Inclusions and coincidences for multiple summing multilinear mappings
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by G. Botelho, H.-A. Braunss, H. Junek and D. Pellegrino

Proc. Amer. Math. Soc. 137 (2009), 991-1000

DOI: https://doi.org/10.1090/S0002-9939-08-09691-3

Published electronically: October 8, 2008

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Abstract:

Using complex interpolation we prove new inclusion and coincidence theorems for multiple (fully) summing multilinear and holomorphic mappings. Among several other results we show that continuous $n$-linear forms on cotype 2 spaces are multiple $(2;q_{k},...,q_{k})$-summing, where $2^{k-1}<n\leq 2^{k}$, $q_{0}=2$ and $q_{k+1}=\frac {2q_{k}}{1+q_{k}}$ for $k\geq 0.$

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