17 февр. 2010 г. · I'm trying to understand his proof that the space of all continuous linear functionals on (X⋆,σ(X⋆,X)) is X.

21 мая 2016 г. · More generally, Nic, if G is a function on X∗ that is weak∗ continuous on bounded sets, and Y is a subspace of X∗ that is invariant under G, ...

2 окт. 2016 г. · so assuming f→ϕ∘f is sequentially continuous wrto the weak topology of L2[0,1]n and taking weak limits we get ϕ(a)=ϕ(a+b)+ϕ(a−b)2. Thus, testing ...

11 апр. 2012 г. · I consider a linear map T:X∗→Y∗, where X∗ and Y∗ are duals of Banach spaces. I would like to know if I can deduce that T is weak* continuous.

7 мая 2017 г. · A function is weakly sequentially continuous iff its restriction to every ball is weakly continuous. You have proved one direction.

4 мая 2014 г. · Note that in this context, weak and strong convergence for sequences coincide. Also the conclusion holds not just for linear functionals but for ...

23 сент. 2020 г. · I'm reading some papers where the condition of weak sequential continuity is crucial instead of the weak continuity.

24 окт. 2017 г. · Let X and Y be separable Banach spaces and consider their dual spaces X∗ and Y∗ equipped with weak* topology. Suppose that a linear map T:X∗→Y∗ is ...

19 июн. 2021 г. · It is a well-known open problem whether there exists an infinite-dimensional amenable Banach algebra whose underlying Banach space is reflexive.

1 нояб. 2012 г. · A linear mapping T:D′(K⊂Ω)→E into any locally convex space E is continuous if it maps convergent sequences to convergent sequences.