What is the meaning of Shaking Sinatra's hand?

Sinatra was a gentleman's gentleman, the guy had class for a rich man, he never looked down his nose to people and he never backstabbed if you went up to him he talked to you like a best friend. If you shook Sinatra's hand its like saying you shook a good mans hand, so for you to backstab someone like, Willie Bank (Al Pacino) did in Oceans Thirteen, is like disrespecting Sinatra, because he shook his hand. The point of the movie is that even rich people have no class even though they claim to.

Frank Sinatra was the actor who played Ocean in the original version of Ocean's 11, so it's really just an in-movie-joke and nod in Ocean's Thirteen.