Al Viola

With Frank Sinatra at the 500 Club in Atlantic City 1961 (pic from official site)
Al Viola, a guitarist who worked with Frank Sinatra for 25 years and also played the mandolin on the The Godfather soundtrack, died last Wednesday. Viola performed with Sinatra at concerts, on recordings and in television specials. He is heard on such Sinatra hits as “My Way” and “New York, New York.”

Watch this clip of the 1966 performance of "Luck Be a Lady" from Frank Sinatra - A Man and His Music Part II - With Special Guest Nancy Sinatra. Viola is to Sinatra's left. You can actually hear his guitar chords (he's playing right on the beat). Note his head and feet movements. That's what taught me "swing."

NY Times obit