This is the last round of questions, I promise.
(1) Identify the space of all continuous linear functionals on the space .
Is Y closed vector space in X? What is the complement of Y?
(3) Prove that the series
converge for every vector
if and only if .
These are the last ones I don't know what to do with, and if anyone has the time and is willing to help, I would be really grateful.