Journal of Topology and Analysis ( IF 0.5 ) Pub Date : 2021-05-05 , DOI: 10.1142/s1793525321500345 Bruno de Mendonça Braga 1 , Gilles Lancien 2 , Colin Petitjean 3 , Antonín Procházka 2
We study the nonlinear embeddability of Banach spaces and the equi-embeddability of the family of Kalton’s interlaced graphs into dual spaces. Notably, we define and study a modification of Kalton’s property that we call property (with ). We show that if equi-coarse Lipschitzly embeds into , then the Szlenk index of is greater than , and that this is optimal, i.e. there exists a separable dual space that contains equi-Lipschitzly and so that has Szlenk index . We prove that does not coarse Lipschitzly embed into a separable dual space by a map with distortion strictly smaller than . We also show that neither nor coarsely embeds into a separable dual by a weak-to-weak sequentially continuous map.
中文翻译:
关于 Kalton 的交错图和非线性嵌入到对偶 Banach 空间中
我们研究了 Banach 空间的非线性可嵌入性和 Kalton 交错图族的等可嵌入性进入双重空间。值得注意的是,我们定义并研究了 Kalton 属性的修改我们称之为财产(和). 我们证明如果等粗 Lipschitzly 嵌入到, 然后是 Szlenk 指数大于,并且这是最优的,即存在一个可分离的对偶空间包含equi-Lipschitzly 所以有 Szlenk 指数. 我们证明不粗糙 Lipschitzly 嵌入到一个可分离的对偶空间中,映射的失真严格小于. 我们还表明,无论是也不通过弱到弱粗略地嵌入到一个可分离的对偶中顺序连续映射。