Common subspaces of L_p-spaces

1992/11/05 by Alexander Koldobsky, Koldobsky, Alexander
Mathematics · #46E #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/9211209

openalex publication_date 1992/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n≥ 2, p<2 and q>2, does there exist an n-dimensional Banach space different from Hilbert spaces which is isometric to subspaces of both L_p and L_q? Generalizing the construction from the paper "Zonoids whose polars are zonoids" by R.Schneider we give examples of such spaces. Moreover, for any compact subset Q of (0,∞)∖ \2k, k∈ N\, we can construct a space isometric to subspaces of L_q for all q∈ Q simultaneously. This paper requires vanilla.sty

Related

• A Banach subspace of L_1/2 which does not embed in L₁ (isometric version)
• Rosenthal operator spaces
• L_p+L_∞ and L_p∩ L_∞ are not isomorphic for all 1≤ p
• Tensor products and independent sums of \Cal L_p-spaces, 1
• Subspace structure of some operator and Banach spaces