科研之友
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摘要
In this article, we characterize the "identity" of an operator space through an analogue of the abstract numerical radius. From this, we give a simple proof of the fact that quotients of unital operator spaces by complete M-ideals are unital. Moreover, we show that both CB(A) and CB(M-*) are unital operator spaces, when A is a C*-algebra and M is a von Neumann algebra. We also show that if X is a normed space with numerical index 1, then CB(max X; min X) is a unital operator space. Using the idea in our characterization, we consider unital tensor products of unital operator spaces.
