@article {
author = {Khorshidvandpour, Sajad and Aminpour, Abdolmohammad},
title = {On the reducible $M$-ideals in Banach spaces},
journal = {Sahand Communications in Mathematical Analysis},
volume = {07},
number = {1},
pages = {27-37},
year = {2017},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2017.23873},
abstract = {The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<\infty)$, then the number of reducible $M$-ideals does not exceed of $\frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The intersection of two $M$-ideals is not necessarily reducible. We construct a subset of the set of all $M$-ideals in a Banach space $X$ such that the intersection of any pair of it's elements is reducible. Also, some Banach spaces $X$ and $Y$ for which $K(X,Y)$ is not a reducible $M$-ideal in $L(X,Y)$, are presented. Finally, a weak version of reducible $M$-ideal called semi reducible $M$-ideal is introduced.},
keywords = {$M$-ideal,Reducible $M$-ideal,Maximal $M$-ideal,$M$-embedded space,Semi reducible $M$-ideal},
url = {https://scma.maragheh.ac.ir/article_23873.html},
eprint = {https://scma.maragheh.ac.ir/article_23873_5d80e8659619ca4eed8588332a074319.pdf}
}