A reflexive Banach space with an uncomplemented isometric subspace

TL;DR

This paper constructs a reflexive Banach space that contains an isometric subspace which is not complemented, providing a new example in the theory of Banach spaces.

Contribution

It introduces a novel reflexive Banach space with an isometric subspace that remains uncomplemented, advancing understanding of subspace complementability.

Findings

Existence of a reflexive Banach space with an uncomplemented isometric subspace

Explicit construction of such a space

Implications for the structure of Banach spaces

Abstract

We construct a reflexive Banach space $X$ with a subspace isometric to $X$, which is not complemented in $X$.