Thanks for driving my attention to them. I was not aware that these symbols ≪≫ are also available as Unicode symbols, but you are right, they are, and, at least "operator≪" looks better in my browser than "operator«". But the former one occupies more horizontal space, which you may not like.
Anyhow, that's a matter of font choice rather than the LaTeX shorthand. Unicode probably does not have a proper symbol for the "output operator".