The Pluripotential Theory, which is a recently developed branch of the theory of functions of several complex variables, has attracted much interest among analysts. In the first part of the talk, we establish a pluripotential theory for Banach lattice valued functions by defining plurisubharmonic functions attaining values in a Banach lattice and a Dirichlet problem for such functions. Then we provide a Perron method of solution for the mentioned Dirichlet problem with continuous boundary data. In the second part, we introduce operator valued Jensen measures, present Edwards’ Theorem for Banach lattice valued functions and lastly explain their possible connection to the Dirichlet problem. 

Joint work with Nihat Gökhan Göğüş (Sabanci University)