Problem of the Week 5

So I thought it would be fun to show some exercises here taken from the FA2 course I did last semester. Instead of writing it all out, I will just link the course page and label the exercise sheet. Exercise 5.4 from...

Solution to Problem of the Week 4

So, this is really late, the semester took its toll on me, and again nothing works. The first problem is an application of the Eberlain-Smulyan theorem; let be a countable dense subset of and note that for each there exists a subsequence such that is weakly...

Solution to Problem 3

So this problem comes from the functional analysis course I took last semester. Although simple, I thought was pretty cool. In the actual exercise they had broken it down into three parts, which I did not show in the problem post. Here I will show the steps as claims....