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It is now well know that the measure algebra [script capital] M ([italic capital] G) of a locally compact group can be regarded as a subalgebra of the operator algebra [italic capital] B ([italic capital] B ([italic capital] L2 ([italic capital] G))) of the operator algebra [italic capital] B ([italic capital] L2 ([italic capital] G)) of the Hilbert space [italic capital] L2 ([italic capital] G). We study the situation in hypergroups and find that, in general, the analogous map for them is neither an isometry nor a homomorphism. However, it is completely positive and completely bounded in certain ways. This work presents the related general theory and special examples.