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In designing a cognitive radio sensor network (CRSN), we need to take account of energy both efficiency and primary user (PU) protection since the CRSN consumes additional energy to support CR functionality such as channel sensing and switching, which can shorten the network lifetime. In this paper, we propose a new channel management scheme for CRSNs, which heightens the energy efficiency while not greatly disturbing a PU. The CRSN with the proposed scheme adaptively selects its operation mode among channel sensing, channel switching, and data transmission/reception, according to the channel-sensing outcome. Considering that the sensing outcome can be erroneous due to noise uncertainty, we design the proposed scheme on the basis of the partially observable Markov decision process framework. The simulation results show that the proposed scheme energy-efficiently operates while properly protecting a PU.