Phillips' Lemma for L-embedded Banach spaces

TL;DR

This paper proves a version of Phillips' lemma for L-embedded Banach spaces, showing that the L-projection in such spaces is weak-weakly sequentially continuous, which advances understanding of their structural properties.

Contribution

The paper introduces a new version of Phillips' lemma specific to L-embedded Banach spaces, highlighting the weak-weak sequential continuity of the L-projection.

Findings

L-projection in L-embedded spaces is weak-weakly sequentially continuous

Provides a new perspective on the structure of L-embedded Banach spaces

Advances theoretical understanding of projections in Banach space theory

Abstract

In this note the following version of Phillips' lemma is proved. The L-projection of an L-embedded space - that is of a Banach space which is complemented in its bidual such that the norm between the two complementary subspaces is additive - is weak-weakly sequentially continuous.