Некоторые специальные свойства функционалов Мазура. II

Abstract

Let $M$ be the set of Mazur's functionals (otherwise - generalized limits). In the article the new approach is suggested and new formulas for the calculation of the function $\tau(x) = sup_{x^*\in M} x^*x$ are obtained. It is proved that $M$ is not weakly compact. The space of almost convergent to zero sequences $ac_0$ is studied. In particular, it is proved that $ac_0$ is not complement at $l_\infty$. Structural properties of the set $M$ are considered. It is proved, for example, that $M$ coincides with the positive part of unit sphere of some $AL$-space.