Frontiers of Mathematics in China >
Possibly non-unital operator system structures on a possibly non-unital function system
Received date: 26 Dec 2011
Accepted date: 20 Feb 2012
Published date: 01 Oct 2012
Copyright
In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.
Jianze LI . Possibly non-unital operator system structures on a possibly non-unital function system[J]. Frontiers of Mathematics in China, 2012 , 7(5) : 847 -855 . DOI: 10.1007/s11464-012-0235-0
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