On the Semadeni derivative of Banach spaces C(K, X)

Autor(es)

Candido, Leandro

• Tipo de documento: Artigo Científico
• Fonte: STUDIA MATHEMATICA; v. 266, n. 2, p. 16-pg., 2022-04-28.

Resumo

The Semadeni derivative of a Banach space X, denoted by S(X), is the quotient of the space of all weak* sequentially continuous functionals in X** by the canonical copy of X. In a remarkable 1960 paper, Z. Semadeni introduced this concept in order to prove that C([0, omega(1)]) is not isomorphic to C([0, omega(1)]) circle plus C([0, omega(1)]). Here we investigate this concept in the context of C(K, X) spaces. In our main result, we prove that if K is a Hausdorff compactum of countable height, then S(C(K , X)) is isometrically isomorphic to C(K, S(X)) for every Banach space X. Additionally, if X is a Banach space with the Mazur property, we explicitly find the derivative of C([0, omega(1)](n), X) for each n >= 1. Further we obtain an example of a nontrivial Banach space linearly isomorphic to its derivative. (AU)

• Processo FAPESP: 16/25574-8 - Geometria dos espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Temático