Skip to main content
edited tags
Link
ABB
  • 4.1k
  • 1
  • 11
  • 19
Source Link
ABB
  • 4.1k
  • 1
  • 11
  • 19

Is the strong operator topology metrizable?

Let $X$ be a separable Banach space. Is the strong operator topology metrizable on $B(X)$, the space of all bounded operators on $X$?

SOT-$\lim T_i=0~$ if and only if $~\lim \|T_ix\|=0$ for every $x\in X$.