I'm trying to find out who owns these items:
2115: Muay Thai Left Foot
2116: Muay Thai Right Foot
2117: Muay Thai head band
2118: Muay Thai Left Armband
2119: Muay Thai Right Armband
2120: Muay Thai Left Hand
2121: Muay Thai Right Hand
Anyone know how to find who owns them? Or maybe someone just knows who it is?

The reason there's isn't a 'search owner by item' function is that people don't want to be harassed about selling their stuff if they're not clearly trying to sell it.
Sure, maybe 1 time in 20 you'll pm someone with an offer and they'll actually take you up on it but with the market board and automated feature the thinking is that if someone hasn't explicitly indicated that they want to sell their stuff then they don't want to sell it or aren't interested.

I just wanted to know if the account was banned or abandoned to see if I could buy them off an admin or something.

Items are only removed from banned or abandoned accounts for sale in some very specific circumstances, the least of which (but not the only required circumstance) is when it is astonishingly clear that the user will never be returning to that account ever.