I am reading the following book:
Optimization by Vector Space Methods written by
D. G. Luenberger
My problem comes from the Example 1. in p.127:
The strong convergence means the convergence in norm. However, we can still define a norm for infinite-dimensional space such as the $l_p$ norm. Therefore, we can still define compactness w.r.t strong convergence in the infinite dimensional spaces.
So I am confused about what did the author try to say.