Smooth p-order ideals in non-unital ordered normed spaces

Abstract

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.