Timeline for A double sequence in a Banach space

11 events

when toggle format	what		by	license	comment
Dec 24, 2017 at 11:10	vote	accept	Matey Math
Dec 24, 2017 at 0:50	answer	added	Mikhail Ostrovskii		timeline score: 3
Dec 21, 2017 at 16:30	comment	added	Matey Math		@PietroMajer thanks for your answer and suggestion
Dec 21, 2017 at 16:29	comment	added	Pietro Majer		To get the conclusion you wish, i would apply a dominated convergence for series, assuming the needed hypotheses.
Dec 21, 2017 at 16:17	comment	added	Pietro Majer		I don't think it is true, if $\dim V>1$: given any $u$ and $u_0$ linearly independent, take $a_{n,m}:=\delta_{n,m}$, and $v_{n,n}:=u$ for all $n$ and $v_{m,n}:=u_0$ for $n\neq m$.
Dec 21, 2017 at 11:50	comment	added	Matey Math		I thing it's true but i can't get the proof... and i need a proof
Dec 21, 2017 at 11:47	comment	added	Michael Renardy		@GeraldEdgar: If V is 1-dimensional and $u_0\neq 0$, isn't it tautologically true that $u=au_0$ for some a? Don't you mean 2-dimensional rather than 1-dimensional?
Dec 21, 2017 at 11:31	history	edited	Matey Math	CC BY-SA 3.0	added 21 characters in body
Dec 21, 2017 at 11:31	comment	added	Matey Math		@GeraldEdgar $V$ is infinite dimensiona, now i edit
Dec 21, 2017 at 11:20	comment	added	Gerald Edgar		Is it true when $V$ is $1$-dimensional? If so, can that be used to prove your case?
Dec 21, 2017 at 10:24	history	asked	Matey Math	CC BY-SA 3.0