At the moment the NotesDatabase class contains a method to create a new Full-Text Index, but only for a Local database, not for remote databases.
Getting access to the current Full-Text Index settings for a NotesDatabase object beyond a boolean that tells me if the db is indexed or ...
In XPages you can easily filter views by using an ftsearch.
Sadly after searching the result is not longer sorted (it sorted by notes-relevance, but nobody knows what that means).
Make this result sortable if the view columns are sortable, like in the notes client, where I can click ...