| Full text | |
| Author(s): |
Candido, Leandro
Total Authors: 1
|
| Document type: | Journal article |
| Source: | STUDIA MATHEMATICA; v. 266, n. 2, p. 16-pg., 2022-04-28. |
| Abstract | |
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) | |
| FAPESP's process: | 16/25574-8 - Geometry of Banach Spaces |
| Grantee: | Valentin Raphael Henri Ferenczi |
| Support Opportunities: | Research Projects - Thematic Grants |