A Banach subspace of L_1/2 which does not embed in L₁ (isometric version)

1994/04/20 by Alexander Koldobsky, Koldobsky, Alexander
Mathematics · #46B #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9404212

openalex publication_date 1994/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every n≥ 3, we construct an n-dimensional Banach space which is isometric to a subspace of L_1/2 but is not isometric to a subspace of L₁. The isomorphic version of this problem (posed by S. Kwapien in 1969) is still open. Another example gives a Banach subspace of L_1/4 which does not embed isometrically in L_1/2. Note that, from the isomorphic point of view, all the spaces L_q with q<1 have the same Banach subspaces.

Related

• Isometric embeddings of compact spaces into Banach spaces
• Common subspaces of L_p-spaces
• Isometric embeddings of separable Banach spaces into (ℓ^∞ ∖ c)∪\0\
• Examples of infinite dimensional Banach spaces without infinite equilateral sets
• Dual Banach spaces which contain an isometric copy of L₁