当前位置: X-MOL 学术Bull. Lond. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Almost everywhere convergent sequences of weak∗‐to‐norm continuous operators
Bulletin of the London Mathematical Society ( IF 0.8 ) Pub Date : 2020-11-25 , DOI: 10.1112/blms.12439
José Rodríguez 1
Affiliation  

Let X and Y be Banach spaces, and T : X Y be an operator. We prove that if X is Asplund and Y has the approximation property, then for each Radon probability μ on ( B X , w ) there is a sequence of w ‐to‐norm continuous operators T n : X Y such that T n ( x ) T ( x ) 0 for μ ‐a.e. x B X ; if Y has the λ ‐bounded approximation property for some λ 1 , then the sequence can be chosen in such a way that T n λ T for all n N . The same conclusions hold if X contains no subspace isomorphic to 1 , Y has the approximation property (respectively, λ ‐bounded approximation property) and T has separable range. This extends to the non‐separable setting a result by Mercourakis and Stamati.

中文翻译:

弱范数到范数连续算子的几乎所有收敛序列

X ÿ 是Banach空间,并且 Ť X ÿ 成为运营商。我们证明 X 是Asplund和 ÿ 具有近似属性,那么对于每个Radon概率 μ X w 有一个序列 w 规范的连续运算符 Ť ñ X ÿ 这样 Ť ñ X - Ť X 0 为了 μ ‐ae X X ; 如果 ÿ λ 某些的有界近似属性 λ 1个 ,那么序列可以这样选择: Ť ñ λ Ť 对全部 ñ ñ 。如果得出相同结论 X 不包含与的同构子空间 1个 ÿ 具有近似属性(分别是 λ 有界的近似属性)和 Ť 具有可分离的范围。这延伸到了Mercourakis和Stamati提出的不可分割的设置。
更新日期:2020-11-25
down
wechat
bug