Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces

This work provides a framework to treat optimal control problems on separable Banach spaces in the viscosity sense. First, it extends the notion of $B$-viscosity solutions to the Banach setting and relates the extension to the notions of viscosity solutions used in metric space settings. As the main results, the paper proves a strict comparison principle and characterizes the value function of an optimal control problem as the unique viscosity solution to an infinite-dimensional HJB equation.