An ideal K of R is a subset that is both a left ideal and a right ideal of R. For emphasis, we sometimes call it a two-sided ideal but the reader should understand that unless qualified, the word ideal will always refer to a two-sided ideal. The zero ideal (0) and the whole ring R are examples of two-sided ideals in any ring R. A (left)(right) ideal I such that I 6= R is called a proper (left)(...

In [4], the notion of a complete one-sided M-ideal for an operator space X was introduced as a generalization of Alfsen and Effros' notion of an M-ideal for a Banach space [1]. In particular, various equivalent formulations of complete one-sided M-projections were given. In this paper, some sharper equivalent formulations are given in the special situation that X = A, a C *-algebra (in which ca...

We consider the problem of estimating a one-dimensional parameter θ in a smooth parametric model when deviations from the “true” θ have to be judged in an asymmetric way, because underestimation is no problem while overestimation is. In the infinitesimal robust setup, we solve a corresponding asymmetric problem for as. linear estimators Sn : min asVarid(Sn) s.t. supQn asBiasQn(Sn) ≤ b for some ...

In [4], the notion of a complete one-sided M -ideal for an operator space X was introduced as a generalization of Alfsen and Effros’ notion of an M -ideal for a Banach space [1]. In particular, various equivalent formulations of complete one-sided M -projections were given. In this paper, some sharper equivalent formulations are given in the special situation that X = A, a C∗-algebra (in which ...