1
$\begingroup$

It is true that strong operator topology is defined to make sense pointwise limit in von Neumann algebra and weak operator topology is defined for getting compactness on unit ball, ultraweak topology is defined to get compatibility in predual, why are the either 5 topologies defined to get more information about the algebra? Can I have more general clarity on these?

$\endgroup$
2
  • 2
    $\begingroup$ I think this question will be easier to answer if you listed the eight topologies you are referring to. $\endgroup$
    – Adrián González Pérez
    Commented Jul 15, 2018 at 13:34
  • $\begingroup$ According to Takesaki volume 1, they are (i)$\sigma$ -strong*, (ii)$\sigma$-strong, (iii)$\sigma$-weak,(iv)strong*,(v)strong,(vi)weak,(vii)uniform/norm topologies $\endgroup$
    – mathlover
    Commented Jul 15, 2018 at 18:27

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .