Let denote the space of sequences such that , equipped with the norm . Let denote the usual norm on .
Show that , and hence deduce that .
Any help would be appreciated. Thanks in advance
Just think that means that is finite, and the same for with . You can look your geometric argument by the point of view that there are vectors with "infinity length" with the measure , but with finite length with the smaller masure , as for example . The contrary is not possible because this inequality