  We define an infinite dimensional modification of lower-semicomputability of
density operators by G\'acs with an attempt to fix some problem in the paper.
Our attempt is partly achieved by showing the existence of universal operator
under some additional assumption. It is left as a future task to eliminate this
assumption. We also see some properties and examples which stimulate further
research. In particular, we show that universal operator has certain nontrivial
form if it exists.
