Meaning of notation "$\overline{ran}$", as in "$\overline{ran \rho}\subset\overline{ran\sigma}$" (from an article about quantum entropy)

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When I look up to an article about quantum entropy, I found this "$\overline{ran}$" notation.

https://i.stack.imgur.com/NNPdl.jpg

When I try to search on google about "Ran" in mathematics, it leads me to the Ran space, but I'm sure that's not what I'm looking for.

So, what does the "$\overline{ran}$" notation mean?