论文标题
免费的双空间和免费的Banach格子
Free dual spaces and free Banach lattices
论文作者
论文摘要
阐明了由Banach空间产生的免费Banach晶格与自由双空间之间的关系。特别是，这表明，对于每个Banach空间$ e $，免费$ P $ -Convex Banach晶格由$ e^{**} $产生在$ fbl^p [e] $中表示。此外，我们还表明，对于$ p> 1 $，$ fbl^p [e]^{**} $实际上被视为由$ e $产生的免费双$ p $ -p $ -convex banach晶格，而对于$ p = 1 $，当$ e $不包含$ \ ell_1 $的互补副本时，这会发生准确地发生。
The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space $E$ the free $p$-convex Banach lattice generated by $E^{**}$, denoted $FBL^p[E^{**}]$, admits a canonical isometric lattice embedding into $FBL^p[E]^{**}$ and $FBL^p[E^{**}]$ is lattice finitely representable in $FBL^p[E]$. Moreover, we also show that for $p>1$, $FBL^p[E]^{**}$ can actually be considered as the free dual $p$-convex Banach lattice generated by $E$, whereas for $p=1$ this happens precisely when $E$ does not contain complemented copies of $\ell_1$.
