These adaptors are 'smart', i.e. they contain electronics to do the
conversion, so as with hardware generally with linux, what counts is
the chipset. I believe that many of these devices use the Prolific
PL2303 chipset, which shows up with 'lsusb', at least in my case, as
"ID 067b:2303 Prolific Technology, Inc. PL2303 Serial Port". This
chipset has kernel support via the pl2303 driver. I have another
adaptor whose ID apparently isn't in the database; nothing shows up
other than the numerical ID. It is also grabbed by pl2303 (although
IIANM, that wasn't the case several months ago, when I first acquired
it), but it doesn't seem to be working properly, as opposed to the
Prolific one, which works fine.
I purchased both my adaptors on Ebay. They are virtually identical in
appearance, except for color; both have attractive silver cables