@MartinSleziak @JeremyRickard I was going to reply to your meta "post" before you deleted it, but basically the question itself and the way it was asked smelled to me of "graduate student in North America needs to revise for some kind of qualifier or comprehensive exam". I could be wrong, of course, but somehow this very nice application of BCT has become known as "standard exercise for students at a certain level".
Note for other reading: in my (limited) experience, this is a very standard question in certain kinds of graduate school programmes, sometimes accompanied by a hint such as "use the Baire category theorem" — Yemon Choi7 mins ago
I hope that the links from my comments and Yemon Choi's comment will help the OP.
I guess the question would be fine at math.SE, maybe after adding some context. AFAICT the only difference from the already linked questions is that many posts have $\lim_{n\to \infty}f(nx)=0$ for every $x\in\mathbb R$. Here we have $x\in[0,1]$.
OTOH occasionally even questions which can be assigned to students in the first year at university are well received and upvoted here on MO. (I guess it mostly depends on whether there are interesting/clever/ingenious answers.)
One of the perks of becoming moderator is that you get superping. I am not sure whether mods use it that often - I think regular users like me can live just fine even without it.
Do there exist two Banach lattices which are linearly isometric but not Banach-lattice isometric? This is so basic that you would expect a textbook or monograph to have answered this, but I have not seen it.
Do there exist two Banach lattices which are linearly isometric but not Banach-lattice isometric? This is so basic that you would expect a textbook or monograph to have answered this, but I have not seen it.
