TY - JOUR
AU - Karl-Mikael Perfekt
PY - 2017/09/22
Y2 - 2021/02/25
TI - On M-ideals and o-O type spaces
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 121
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-96626
UR - https://www.mscand.dk/article/view/96626
AB - We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.
ER -