On the complemented subspaces of X_p

1990/07/20 by Dale E. Alspach, Alspach, Dale E.
Mathematics · #46B #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B

paper · pdf · doi:10.48550/arxiv.math/9201214

arxiv created 1990/07/20 · openalex publication_date 1990/07/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove some results related to the problem of isomorphically classifying the complemented subspaces of X_p. We characterize the complemented subspaces of X_p which are isomorphic to X_p by showing that such a space must contain a canonical complemented subspace isomorphic to X_p. We also give some characterizations of complemented subspaces of X_p isomorphic to ℓ_p⊕ ℓ₂.

Related

• Classifying Complemented Subspaces of L_p with Alspach Norm
• Complemented Subspaces of L_p Determined by Partitions and Weights
• Complemented subspaces of Banach lattices
• The complemented subspace problem for C(K)-spaces: A counterexample
• On isometric stability of complemented subspaces of L_p