The concept of operator is exceedingly important in many areas as a tool of theoretical studies and practical applications. Here, we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, networks, and processes. In particular, the operator approach allows for the solving of many computing problems in a more general context of operating spaces. In addition, operator representation of computing devices and their networks allows for the construction of a variety of operator compositions and the development of new schemas of computation as well as network and computer architectures using operations with operators. Besides, operator representation allows for the efficient application of the axiomatic technique for the investigation of computation.
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