Characterizations of Ordered Self-adjoint Operator Spaces
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Publication:6264853
DOI10.1007/S11785-022-01317-5arXiv1508.06272MaRDI QIDQ6264853
Publication date: 25 August 2015
Abstract: We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as -vector spaces equipped with a matrix gauge structure. We explain how this perspective has several advantages over other notions of non-unital operator systems in the literature. In particular, the category of matrix gauge -vector spaces includes injective objects and a Webster-Winkler-type duality theorem, both of which we show generally fail with other notions of non-unital operator systems. As applications, we characterize those subspaces of operator systems which are kernels of completely positive maps and define a new operator space structure on the matrix ordered dual of an operator system generalizing the classical notion of a base norm space.
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