Standard Duals of Operator Bimodules

In this paper, we introduce the notion of standard duals of operator bimodules. They coincide with the standard duals of operator spaces when the operator bimodules are nothing more than operator spaces. Using the Haagerup tensor product of operator sesquimodules and operator bimodules, we give a representation for the standard duals of operator bimodules in terms of the operator space standard duals. We also study the problem whether an operator bimodule is completely isometrically embedded in its second standard dual and its connection with the behavior of the adjoint operation. In addition, we also find out the standard dual of a direct limit of a sequence of operator bimodules.