The purpose of this paper is to study theory of two different kinds of a-layer order-preserving operator space, namely, ?a-opos and\r\n?*\r\na ()-opos. The former kind of space is formed by a-layer function in L-fuzzy order-preserving operator space. The later kind\r\nof space is derived by local a-remote neighborhood function, which is related with ?a-opos and a-ideal. We study characteristic\r\nproperties of the two kinds of spaces, respectively, and give some applications to show the intimate relations under two different\r\n?*\r\na ()-oposs.
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