L- and M-structure in lush spaces

TL;DR

This paper investigates lush Banach spaces and demonstrates that lushness is preserved in subspaces that are either L-summands or M-ideals, expanding understanding of lush space structure.

Contribution

It proves that subspaces of lush Banach spaces that are L-summands or M-ideals are also lush, revealing new structural properties.

Findings

Lushness is preserved in L-summands of lush spaces

Lushness is preserved in M-ideals of lush spaces

Provides new insights into the structure of lush Banach spaces

Abstract

Let $X$ be a Banach space which is lush. It is shown that if a subspace of $X$ is either an L-summand or an M-ideal then it is also lush.