Is there a legal way to play Mario on PS2?

I have a PS2 and want to play the classic Mario games on it. I know the PS2 is a Sony product and Mario is a Nintendo product, but that doesn't answer my question because I have seen some non-Sony games made for PS2. So, I am wondering if they made a Mario game for PS2?

When I googled "PS2 Mario" some images came up of a PS2 version of the Mario collection, so I thought the answer was "yes". But then I also came across some forum posts saying this did not exist, so I thought the answer was "no". Then I came across some places where you can buy or download the Mario collection for PS2, but I couldn't tell if it was a legit (authorized, legal) product.

I'm not looking for a hack that someone came up with in their basement; I'm wondering if they actually made a (legal) game for PS2 in which you can play Mario. Thanks!

No there is no legit Mario game for any console other than that of Nintendo. I have no firm proof to link you to but I can say that Mario is wholly owned by Nintendo whereas as the non-Sony games you allude to for the PS2 are made by companies not directly related to any console manufacturer and the likelihood of Nintendo making a game for a console other than their own is akin to pigs flying.