Ultrastrong topology

In functional analysis, the ultrastrong topology, or σ-strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the family of seminorms

for positive elements ${\displaystyle \omega }$ of the predual ${\displaystyle L_{*}(H)}$ that consists of trace class operators. ^: 68

It was introduced by John von Neumann in 1936.