Isometric F-spaces of log-integrable function

2019/09/26 by R. Z. Abdullaev, Abdullaev, R., Vladimir Chilin +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1909.11876

openalex publication_date 2019/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (Ω_i,\mathcal A_i,μ_i) be a measure space with finite measure μ_i, and let (L_log(Ω_i, \mathcal A_i,μ_i), ‖⋅‖_log,μi) be a F-space of all log-integrable functions on (Ω_i,\mathcal A_i,μ₁), i =1, 2 . It is proved that F-spaces (L_log(Ω₁, \mathcal A₁,μ₁), ‖⋅‖_log,μ1) \and (L_log(Ω₂, \mathcal A₂,μ₂), ‖⋅‖_log,μ2) are isometric if and only if there exists a measure preserving isomorphism from (Ω₁, \mathcal A₁,μ₁) onto (Ω₂, \mathcal A₂,μ₂).

Related

• Isomorphisms and isometries of F-spaces of log-integrable measurable functions
• Isometries of generalized log-spaces
• Isometric stability property of certain Banach spaces
• Characterizations of signed measures in the dual of BV and related isometric isomorphisms
• Surjective isometries on rearrangement-invariant spaces