to establish that it owns or controls a qualified investment.

[Alex15]

Claimant has not made any attempt to establish, even prima facie, that it owns or controls a qualified investment. Apart from conclusory allegations, no documentation whatsoever has been supplied establishing Claimant’s alleged shareholding in Yukos or the beneficial ownership thereof.

[kwatts59]

The claimant did not try to make known, that it owns or controls a qualified investment.

In this sentence "to establish" means "to make known"
"prima facie" is a latin term for "on the face" or "obvious" so I think this means the claimant showed no obvious effort.
I do not know why they use the pronoun "it". This sounds very strange.

[Ash]

Probably because the Claimant is not a human being but a legal entity

[kwatts59]

Ah, that makes sense.

[V]

тут просто "доказать", "продемонстрировать"

Алекс, что же Вы так клиентов-то светите нещадно? Некотрые ведь и обидеться могут, ... да и канделябром...
:-)

("а клейманты в этом споре, кстати, как известно, - иностранные акционеры" - из газет)