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

摘要

We introduce smooth p-order ideals (1 <= p <= infinity) 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 smooth1-order ideal. Moreover, we derive that every smooth infinity-order ideal is an L-summand in order smooth 1-normed space.