'así como las realizadas por cuenta propia' = 'as the ones done by itself'
the entire paragraph would maybe go as:
'la caixa joined today the new york stock exchange, one of the main mundial stock platforms, with which it will be able to operate directly for its clients' operations, as well as by itself, ...informed today the [caja de ahorros] (sorry, don't know the real term)'.
i don't know if you're using newspapers for learning spanish but... if that's the case, then it's a hard way to learn! even for us its hard sometimes to read those overly complex sentences, which use rare words that don't really add much to the meaning :)
a little note about 'asi como las realizadas por cuenta propia' though...
it'd be way more natural if it said 'asi como TAMBIEN las realizadas por cuenta propia'.
TAMBIEN meaning 'also'.
i'll go word per word just i case you still have doubts :)
así como = [in the same way as...]
las realizadas = the [ones] done (verb is 'realizar', 'to get something done'. here seen as past tense)
por = in this case, 'by'.
cuenta propia = this is pretty much a 'set phrase'. it means 'itself', though literally it says 'own account'
hoping this helps :)