Do exercises

4.0.21,5.1.4,5.3.3,5.4.3,5.4.4,6.1.2,7.1.9,7.1.18,7.1.23

Show that B(H) is not separable in the norm topology if 
dim(H) = infinity.

Let A be a unital C^*-algebra on H and M is its
strong closure, show that the unitary group of A is 
strongly dense in the unitary group of M.