Let $n\geq 2$ be a natural number, $1\leq p\leq \infty $ and $X$ a Banach space. We prove that if $X^{\ast }$ contains $\lambda $-uniformly copies of $ l_{p}^{k}$, then:
(i) $\mathcal{P}\left( ^{n}X\right) $ contains $c_{\mathbb{K} }\lambda ^{n}$-uniformly copies of $l_{\left( \frac{p^{\ast }}{n}\right)
^{\ast }}^{k}$ in the case $p^{\ast }>n$;
(ii) $\mathcal{P}\left( ^{n}X\right) $ contains\textit{\ }$\lambda ^{n}$ \textit{-}uniformly copies of $l_{\infty }^{k}$ in the case $p^{\ast }\leq n. $ This complete a result of S. Dineen's from 1995.
Dumitru POPA
. UNIFORMLY COPIES OF $l_{P}^{N}$ IN THE SPACES OF POLYNOMIALS[J]. Acta mathematica scientia, Series B, 2026
, 46(1)
: 112
-118
.
DOI: 10.1007/s10473-026-0107-4
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