This paper addresses the slicing of radio access network resources by multiple tenants, e.g., virtual wireless operators and service providers. We consider a criterion for dynamic resource allocation amongst tenants, based on a weighted proportionally fair objective, which achieves desirable fairness/protection across the network slices of the different tenants and their associated users. Several key properties are established, including: the Pareto-optimality of user association to base stations, the fair allocation of base stations' resources, and the gains resulting from dynamic resource sharing across slices, both in terms of utility gains and capacity savings. We then address algorithmic and practical challenges in realizing the proposed criterion. We show that the objective is NP-hard, making an exact solution impractical, and design a distributed semi-online algorithm, which meets performance guarantees in equilibrium and can be shown to quickly converge to a region around the equilibrium point. Building on this algorithm, we devise a practical approach with limited computational information and handoff overheads. We use detailed simulations to show that our approach is indeed near-optimal and provides substantial gains both to tenants (in terms of capacity savings) and end users (in terms of improved performance).