Smooth \(p\)-order ideals in non-unital ordered normed spaces. (English) Zbl 1477.46019
Summary: We introduce smooth \(p\)-order ideals \((1\le p\le \infty)\) to initiate the studies of ideals in non-unital ordered normed spaces. We obtain some order-theoretic properties and examples of these ideals. Furthermore, we show that every semi-\(M\)-ideal in affine space \(A(K)\) is smooth \(\infty \)-order ideal. Moreover, we derive that every smooth 1-order ideal is an \(L\)-summand in order smooth 1-normed space.
Keywords:
ordered normed space; operator system; \(A(K)\)-space; order ideal; \(M\)-ideal; \(L\)-summandReferences:
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