The pointwise James type constant

In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all x ∈ X , ∥ x ∥ = 1, We show that in almost transitive Banach spaces, the map x ∈ X , ∥ x ∥ = 1 ↦ J ( x, X, t ) is constant. As a consequence and having in mind the Mazur’s rotation probl...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2023-06, Vol.49 (2), p.651-659
Main Author: Rincón-Villamizar, M. A.
Format: Article
Language:English
Subjects:
Analysis
Banach spaces
Mathematics
Mathematics and Statistics
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Summary:In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all x ∈ X , ∥ x ∥ = 1, We show that in almost transitive Banach spaces, the map x ∈ X , ∥ x ∥ = 1 ↦ J ( x, X, t ) is constant. As a consequence and having in mind the Mazur’s rotation problem, we prove that for almost transitive Banach spaces, the condition J ( x , X , t ) = 2 for some unit vector x ∈ X implies that X is Hilbert.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-023-0221-7