I thought either Ted Bundy or John Wayne gacy but it isn't saying so in their Bios. Was it one of the gangsters from the 40s, cos it is a song from that era.
Al Jolson (1886-1940) made this song famous - the earliest recording I can find is one he made in June 1926. This was when he was still in vaudeville (music-hall) and before he kicked off sound films the following year!