Possibly scale, but whatever the bug, you need to eradicate it! Start with using a sponge soaked in alcohol and 'paint' all surfaces of the leaves. Then use a horticultural oil spray and spray the plant down, even down into the crown. Repeat every week or so. If that doesn't work, throw it out and begin over with new plant. Keep your plant quarantined from any others.

could we see a pic of the whole ...

palms shed leaves .. fronds i suppose.. yearly ... it is the oldest ones.. outer most ... and usually in winter .... or shortly thereafter ...

and not unlike deciduous trees.. the dead leaves can get pretty funky before removal or shedding ...

that is not to say.. something else isnt going on ... but perhaps there is more than one thing going on ...

how does the new center growth look??? ... is it affected... or looking good.. hence the further pic ... [on rereading i see its not great either...]

finally.. many of the problem bugs exude honeydew ... a sugary substance.. and often the ants harvest such ... the ants are usually what catches our eye.. to find the real culprit ... but the ants are really not a problem at all .. in regard the plant ...but yikes... we dont want them in the house ...

more finally ... lol ... if you are in a warm enough area.. you might want to isolate this outside... in full shade.. until we figure this out.. and what to do about it ...

sometimes.. its just easier to get rid of the whole mess .. if its not some treasured plant.. like grandmas.. or something like that.. otherwise... palms shouldnt be that rare that you need to spend a hundred bucks trying to cure and save a $20 plant.. if you get my drift ...

ken

ps: also. what 'soap' did you use ... when such is suggested.. they mean horticultural soap.. not you common dish DETERGENT ... which can severely harm tender leaves .. of which i never thought of palm as being tender ... but thats another episode ...