论文标题
当地的Banach空间二分法
Local Banach-space dichotomies and ergodic spaces
论文作者
论文摘要
我们证明了Gowers的Ramsey型定理的本地版本[Ann。数学。 156（2002）]以及本地版本的Gowers [Ann。数学。 156（2002）]和第三次二分法（由于Ferenczi-Rosendal引起的“最小/紧密”二分法）[J.功能。肛门。 257（2009）]。这意味着我们获得了这些二分法的版本，这些版本仅限于某些称为d型荷属的子空间，其中给了几个具体的例子。作为一个主要的例子，非希尔伯特式的空间形成了D型家庭；因此，非希尔伯特式空间的上述特性版本出现在新的Banach空间二分法中。结果，我们获得了有关非希尔伯特式巴拉赫空间子空间数量的新信息，从而朝着Ferenczi-Rosendal和Johnson的问题方面的“千古”猜想做出了一些进展。
We prove a local version of Gowers' Ramsey-type theorem [Ann. Math. 156 (2002)], as well as local versions both of the Banach space first dichotomy (the "unconditional/HI" dichotomy) of Gowers [Ann. Math. 156 (2002)] and of the third dichotomy (the "minimal/tight" dichotomy) due to Ferenczi-Rosendal [J. Funct. Anal. 257 (2009)]. This means that we obtain versions of these dichotomies restricted to certain families of subspaces called D-families, of which several concrete examples are given. As a main example, non-Hilbertian spaces form D-families; therefore versions of the above properties for non-Hilbertian spaces appear in new Banach space dichotomies. As a consequence we obtain new information on the number of subspaces of non-Hilbertian Banach spaces, making some progress towards the "ergodic" conjecture of Ferenczi-Rosendal and towards a question of Johnson.
