3
$\begingroup$

I need a help to prove that statement: if $\{e_n\}$ an orthonormal basis in Hilbert space $H$ and $A$ is a compact operator from $H$ to $H$, then $Ae_n\rightarrow 0$. Thx for any help.

  • 1
    Try to calculate the distance between the elements $\{e_n\}$ and after calculate $A(e_n-e_m)$2012-05-22
  • 1
    What characterizations of compact operators do you know? (Hint: Maybe think about the weak topology on $H$.)2012-05-23
  • 0
    @matgaio can you please elaborate?2016-11-09
  • 0
    the square of the distance is 2 but how does that help?2016-11-09

3 Answers 3