Contractive idempotents on locally compact quantum groups
  A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established. 
Matthias Neufang, Pekka Salmi, Adam Skalski and Nico Spronk
math.OA math.QA