Eduardo, it is very hard to say what the tiny white spots that you see appearing on your star are from here. Hopefully it is not the result of dead tissue appearing from an osmotic shock, but the area that went from a while patch to "looking dissolved" sure sounds that way. Given that both of your stars have shown signs of it within a short period of time, it may be that they went through the same salinity change or other osmotic shock a few weeks ago. Were they introduced at the same time, or did your tank go through a large salinity change about then?
Osmotic shock is more of an issue for some stars than others. Many intertidal stars do not seem to suffer greatly from salinity changes, but subtidal stars often have this problem. Even among the subtidal stars, some seem able to lose a small portion to the shock, but recover on their own if left alone (such as it sounds that your unidentified Atlantic star has). Others, such as the blue
Linckia do not seem so fortunate. For what ever reason, blue
Linckia seem to be particularly sensitive to osmotic shock, and they often start to show these white patches of necrotic tissue a few weeks after their exposure. Frequently these white patches spread rapidly as the star begins to dissolve and soon dies. Unlike your Atlantic star, I have not heard of any cases of a
Linckia which had begun to dissolve spontaneously recovering. Sadly, once a
Linckia starts to dissolve, it is usally the beginning of the end for these beautiful animals.
In terms of treatment, many have been proposed, but none seem to work in even the majority of cases, and so the jury is still out on what to do about this event should you encounter it in your tank. The only uniformly useful treatment seems to be prevention -- make sure you do not shock your animal when transporting it or doing water changes, etc. Some people have reported success by amputating the effected area of the star and allowing the rest to recover. Again, this is unpredictable in its success, and some people feel that this rough treatment simply sped the inevitable and pushed the star over the edge, causing it to die more quickly. However, others argue that if there is any chance of saving the star, it is worth the risk, and this is one possibility. Iodine dips and various other treatments have been tried with about the same rate of failure - there is still no good answer for you in terms of what to do.
If you decide to amputate, there is a nice set of pictures by GobyGirl on her amputation of an arm from her
Linckia with the patrasitic snail
Thyca embedded in it online
here, and some follow up on the subsequent recovery of the star
here. If you decide that is a little drastic for you, then you may as well try your isolation in a bowl technique. Perhaps the star will recover, and if my guess is right about the cause, then you have nothing to lose by trying...
Good luck,
Rob