| Full text | |
| Author(s): |
Rincon-Villamizar, M. A.
Total Authors: 1
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| Document type: | Journal article |
| Source: | ANALYSIS MATHEMATICA; v. 49, n. 2, p. 9-pg., 2023-06-01. |
| Abstract | |
In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all x is an element of X, parallel to x parallel to = 1, J(x, X, t) = {sup(parallel to y parallel to=1) (parallel to x + y parallel to(t) + parallel to x - y parallel to(t)/2)(1/t), t is an element of R; sup(parallel to y parallel to=1) (root parallel to x + y parallel to parallel to x - y parallel to, t = 0; sup(parallel to y parallel to=1) min {parallel to x + y parallel to, parallel to x - y parallel to, t = -infinity. We show that in almost transitive Banach spaces, the map x is an element of X, parallel to x parallel to = 1 bar right arrow 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) = root 2 for some unit vector x is an element of X implies that X is Hilbert. (AU) | |
| FAPESP's process: | 21/01144-2 - Ideals associated to sequences in Banach spaces and Lipschitz derivations in Hilbert spaces |
| Grantee: | Michael Alexánder Rincón Villamizar |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |