On maximal Lindenstrauss spaces

Petr Petráček and Jiří Spurný

Vol. 276 (2015), No. 1, 249–256

DOI: 10.2140/pjm.2015.276.249

Abstract

We solve a problem of Lacey (1973) by showing that there exist a metrizable compact space $K$ and a closed space $\mathcal{\mathscr{H}}\subset \mathcal{C}\left(K\right)$ containing constants with $\overline{{\partial }_{\mathcal{\mathscr{H}}}K}=K$ such that $\mathcal{\mathscr{H}}$ is maximal with respect to ${\partial }_{\mathcal{\mathscr{H}}}K$ and $\mathcal{\mathscr{H}}$ is not a Lindenstrauss space.

Keywords

Lindenstrauss space, $L_1$-predual, function space

Mathematical Subject Classification 2010

Primary: 46B25

Milestones

Received: 5 May 2014

Accepted: 23 December 2014

Published: 1 July 2015