Not many are convinced about the quality of capital use among SOEs, given the fact that some have invested heavily in businesses outside of their expertise, with the debt-laden Vinashin being an obvious example.
I am not sure if the “convinced” is an adjective or a verb in passive voice. I tend to think it is an adjective because it seems that there are no obvious agents here.
Apparently, “convinced” could be the past participle of the verb “to convince” functioning here as a part of the predicative adjectival phrase functioning as a subject complement.
I prefer the sentence written the way below
Given the fact that some have invested heavily in businesses outside of their expertise - with the debt-laden Vinashin being an obvious example - not many are convinced about the quality of capital use among SOEs.