23 апр. 2019 г. · I am trying to prove or disprove the following: if the sequence (Tn) converges pointwise to T, i.e. ||Tnx−Tx||B→0 for each x∈A, then (Tn) ...

17 апр. 2011 г. · An example shows that even for continuous functions on a compact set, pointwise convergence doesn't imply convergence in the sup-norm.

28 апр. 2012 г. · Convergence in Lp norm implies pointwise convergence almost everywhere? 2 · L^p convergence => a.e. convergence? 2 · Whether convergence in L2 ...

23 мар. 2021 г. · Pointwise convergence implies convergence in the norm · 2 · Do pointwise convergence and norm boundedness imply Lp convergece? 1 · Pointwise ...

12 мар. 2021 г. · Proof. First let (fn)n∈N converge uniformly to f, all functions from metric space (X,dX) to (Y,dY) belonging to some function space, call it C.

1 сент. 2017 г. · Yes, the norm is always continuous. But this would require that you already know fn→f in ...

15 мая 2020 г. · The question asks to show (an)n converges to a "for the norm topology of B(V,W)". I am not sure what that last bit means. I initially assumed it ...

13 июл. 2013 г. · Let fn be a sequence of functions in Lp(E), 1<p<∞, which converge almost everywhere to a function f in Lp(E), and suppose that there is a ...

15 нояб. 2013 г. · Up to a subsequence it is true. It is usually proved as a by-product of the completeness of Lp.

27 окт. 2017 г. · I want to show that operator norm convergence implies pointwise convergence. Suppose we are looking at the space L(X,Y) i.e the space of all ...