What is the topology on K? It is the compact-open topology, right? So think about what an open set looks like in K. That should give you an idea of how to form an uncountable number of non-intersecting open balls.
Let T: l^2 -> l^2 be bounded linear operators. K=L(l^2,l^2) be the space of T, Prove that K=L(l^2,l^2) is not separable
I know that if a space contains an uncountable number of non intersecting open balls then it is not separable. But how can I apply this statement here ( I mean how to construct such open balls) And are there any easier way to do it ???