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Possibly non-unital operator system structures on a possibly non-unital function system |
Jianze LI() |
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China |
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Abstract 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.
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Keywords
Possibly non-unital function system
operator system
possibly nonunital operator system
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Corresponding Author(s):
LI Jianze,Email:lijianze@yeah.net
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Issue Date: 01 October 2012
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