Inclusion of $L^p$ spaces for functions has been discussed here.
Does this apply to $l^p$ space of sequences similarly?
I tried to show the following: For $1\leq p<q<\infty$, $l^q\subset l^p$ By using Hölder inequality but it doesn't seem to work.
My question is that is this true? If yes, what's the right way to prove it and what's a good counter example for showing $l^p\subset l^q$ is not true? Thanks.