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Abstract Characterizations of Ordered Operator Spaces
We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). We define matrix gauges and demonstrate an abstract characterization of operator spaces in terms of matrix gauges. We show that both characterizations preserve the structure of the self-adjoint, positive, and accretive operators, as well as the operator norm. We show that the order and norm structures on operator spaces are induced by matrix gauges, although inducing matrix gauges are not unique in general. As applications, we study a few special cases of matrix gauge spaces, prove a generalization of the Arveson extension theorem, and study quotients of ordered operator spaces.
Russell, Travis B, "Abstract Characterizations of Ordered Operator Spaces" (2017). ETD collection for University of Nebraska - Lincoln. AAI10269557.