Network functions virtualization (NFV) has become a strategic tool that facilitates mobile network resource sharing and management by mobile network operators (MNOs). Cloud radio access network (C-RAN) virtualization allows agglomeration of multiple radio access networks (RANs) functions in a single resource pool. In this paper, Virtualized Radio Access Network (VRAN) is utilized as the enabler of inter-operator traffic offloading. To explore the energy saving potential of sleep mode scheme in base stations of cooperating MNOs, we leverage on inter-band non-contiguous carrier aggregation and put forward spectrum sharing into private and shared bands. We formulate an optimization problem to obtain the optimal intra-operator and inter-operator beamforming design for realizing energy-efficient virtual RAN. Inter-operator base station load transfer algorithm is proposed as well as inter-operator BS sleep-mode energy saving algorithm. Simulations results show a significant reduction of total inter-operator power consumption as compared to other algorithms.