A Pluripotential Theory For Banach Lattice Valued Functions

In this thesis, we establish a foundation of a pluripotential theory for functionsattaining values in a Banach lattice. For this purpose, we generalize notions suchas semi-continuity, subharmonicity, plurisubharmonicity and maximality for vectorvalued functions, study their properties and the cones of plurisubharmonic functions.Moreover, we investigate operator valued Jensen measures for a given cone of vectorvalued functions, and upper, lower envelopes of a given function with respect tothe given cone. With these at our disposal, we prove Edwards’ Theorem in Banachlattice settings. As an result our findings, we provide a Perron method of solution fora Dirichlet Problem for vector valued harmonic/maximal plurisubharmonic functionswith continuous boundary data