Future high-performance network-based applications are delivered over the high-capacity dynamic optical network. Each of these applications requires dedicated network service, which can be provided by the virtual optical network (VON) created by optical network virtualization. The virtualizable bandwidth variable transceiver (V-BVT) is a key enabling technology for optical network virtualization. In this paper, we propose the virtualization of V-BVT to support the virtualization of optical orthogonal frequency-division-multiplexing-based elastic optical network. We present a novel V-BVT architecture, and introduce both online and offline virtualization algorithms for V-BVT. Accordingly, multiple independent but coexisting virtual transceivers that share the same physical transceiver resources are created, in order to serve separate VONs. To guarantee the isolation of the created virtual transceivers together with their quality of transmission (QoT), the impact of physical layer impairments on different V-BVT solutions is also considered and integrated into the virtualization algorithms. In the offline virtualization, both heuristic and integral linear programming methods are proposed, in order to maximize the VON demand accommodation using the given physical V-BVT resources. In the online virtualization, a heuristic method is proposed to accommodate real-time received VON demands. By applying both algorithms, multiple virtual transceivers can be dynamically created based on the bandwidth and QoT of the VON demands. Finally, we evaluate and compare the performance of the proposed algorithms, and also verify the V-BVT transmission performance through simulation studies.