26 апр. 2016 г. · On the other hand, I just read that weak convergence for operators is when y′(Anx)→y′(Ax) for all y′∈X′ and x∈X holds.

15 мая 2017 г. · Weak convergence of Tn to T is equivalent to the convergence of every entry of Mn to the corresponding entry of M together with the fact that ‖T ...

24 мая 2022 г. · According to post, the condition lim‖Anx‖=‖Ax‖ and weak convergence imply the strong convergence for general class of operators.

12 июн. 2017 г. · This sequence converges uniformly to 0, also strongly and weakly because of inclusion relation of the three.

18 янв. 2018 г. · Weak convergence, together with convergence of norms, implies strong convergence in a Hilbert space. Related. 29 · weak ...

10 окт. 2017 г. · I denote the right shift and left shift by R and L, respectively. It is easy to prove that R∗=L (the adjoint of R is L). We have Wm=Rm.

11 дек. 2014 г. · Let H be a Hilbert space and Tn∈L(H). Suppose that for every x∈H we have that Tnx⇀Tx where "⇀" denotes weak convergence. Prove that T∈L(H) and ‖ ...

19 янв. 2016 г. · Since un is weakly convergent then ϕn is point-wise convergent and so it is also point-wise bounded. Therefore UBP uimplies that ϕn is uniformly ...

7 дек. 2019 г. · The answer is yes, weakly convergent operators are bounded. Assume that it is not bounded, that means exists hn such that ‖Thn‖>n for all n∈N, ...

3 нояб. 2018 г. · The weak star convergence of a sequence fn in the topological dual X′ of X is defined as fn(x)→f(x) for all x∈X.