%0 Journal Article
%T On the reducible $M$-ideals in Banach spaces
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Khorshidvandpour, Sajad
%A Aminpour, Abdolmohammad
%D 2017
%\ 07/01/2017
%V 07
%N 1
%P 27-37
%! On the reducible $M$-ideals in Banach spaces
%K $M$-ideal
%K Reducible $M$-ideal
%K Maximal $M$-ideal
%K $M$-embedded space
%K Semi reducible $M$-ideal
%R 10.22130/scma.2017.23873
%X 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.
%U https://scma.maragheh.ac.ir/article_23873_5d80e8659619ca4eed8588332a074319.pdf