Teleoperation is a valuable tool for robotic manipulators in highly unstructured environments. However, finding an intuitive mapping between a human hand and a non-anthropomorphic robot hand can be difficult, due to the hands' dissimilar kinematics. In this paper, we seek to create a mapping between the human hand and a fully actuated, non-anthropomorphic robot hand that is intuitive enough to enable effective real-time teleoperation, even for novice users. To accomplish this, we propose a low-dimensional teleoperation subspace which can be used as an intermediary for mapping between hand pose spaces. We present two different methods to define the teleoperation subspace: an empirical definition, which requires a person to define hand motions in an intuitive, hand-specific way, and an algorithmic definition, which is kinematically independent, and uses objects to define the subspace. We use each of these definitions to create a teleoperation mapping for different hands. We validate both the empirical and algorithmic mappings with teleoperation experiments controlled by novices and performed on two kinematically distinct hands. The experiments show that the proposed subspace is relevant to teleoperation, intuitive enough to enable control by novices, and can generalize to non-anthropomorphic hands with different kinematic configurations.