THE POINTWISE JAMES TYPE CONSTANT

Autor(es)

Rincon-Villamizar, M. A.

• Tipo de documento: Artigo Científico
• Fonte: ANALYSIS MATHEMATICA; v. 49, n. 2, p. 9-pg., 2023-06-01.

Resumo

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)

• Processo FAPESP: 21/01144-2 - Ideais associados a sequências em espaços de Banach e derivações Lipschitz em espaços de Hilbert
• Beneficiário: Michael Alexánder Rincón Villamizar
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado