Definitizability of normal operators on Krein spaces and their   functional calculus
  We discuss a new concept of definitizability of a normal operator on Krein spaces. For this new concept we develop a functional calculus $\phi \mapsto \phi(N)$ which is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the Hilbert space situation. 
Michael Kaltenb\"ack
math.FA