Operator space

Summary

An operator space is a closed linear subspace of the algebra of bounded operators on a Hilbert space. It comes with the norms it inherits on all matrices with entries in it. These matrix norms carry more information than the Banach space norm alone. The natural maps between operator spaces are the completely bounded maps, and the theory is often described as a "quantized" Banach space theory. Ruan's theorem characterizes operator spaces abstractly by two axioms on the matrix norms.