On the Banach Problem on Surjections

2002/06/11 by Eugene Tokarev, Tokarev, Eugene
Mathematics · #46B07 #46B10 (Primary) 46A20 #46B20 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories #math.FA #msc:46A20 #msc:46B07 #msc:46B10 #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/0206110

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arxiv created 2002/06/11 · openalex publication_date 2002/06/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Is shown that any separable superreflexive Banach space X may be isometrically embedded in a separable superreflexive Banach space Z=Z(X) (which, in addition, is of the same type and cotype as X) such that its conjugate admits a continuous surjection on each its subspace. This gives an affirmative answer on S. Banach problem: Whether there exists a Banach space X, non isomorphic to a Hilbert space, which admits a continuous linear surjection on each its subspace and is essentially different from l₁?

Citations

• On the complemented subspaces problem

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