The dual of a non-reflexive L-embedded Banach space contains $\ell^\infty$ isometrically.

TL;DR

This paper proves that the dual space of a non-reflexive L-embedded Banach space contains an isometric copy of b5^55, highlighting a structural property of such spaces.

Contribution

It establishes that the dual of any non-reflexive L-embedded Banach space necessarily contains b5^55 isometrically, revealing a new geometric characteristic.

Findings

The dual space contains b5^55 isometrically.

Non-reflexive L-embedded spaces have this specific dual structure.

The result clarifies the geometric structure of these Banach spaces.

Abstract

See title. (A Banach space is said to be L-embedded if it is complemented in its bidual such that the norm between the two complementary subspaces is additive.)