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- W2951670835 abstract "A famous result due to Grothendieck asserts that every continuous linear operator from $ell_{1}$ to $ell_{2}$ is absolutely $(1,1)$-summing. If $ngeq2,$ however, it is very simple to prove that every continuous $n$-linear operator from $ell_{1}times...timesell_{1}$ to $ell_{2}$ is absolutely $(1;1,...,1) $-summing, and even absolutely $(frac{2}% {n};1,...,1) $-summing$.$ In this note we deal with the following problem: Given a positive integer $ngeq2$, what is the best constant $g_{n}>0$ so that every $n$-linear operator from $ell_{1}times...timesell_{1}$ to $ell_{2}$ is absolutely $(g_{n};1,...,1) $-summing? We prove that $g_{n}leqfrac{2}{n+1}$ and also obtain an optimal improvement of previous recent results (due to Heinz Juenk $mathit{et}$ $mathit{al}$, Geraldo Botelho $mathit{et}$ $mathit{al}$ and Dumitru Popa) on inclusion theorems for absolutely summing multilinear operators." @default.
- W2951670835 created "2019-06-27" @default.
- W2951670835 creator A5069684691 @default.
- W2951670835 date "2011-02-22" @default.
- W2951670835 modified "2023-09-27" @default.
- W2951670835 title "On cotype and a Grothendieck-type theorem for absolutely summing multilinear operators" @default.
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