| Full text | |
| Author(s): |
Candido, Leandro
Total Authors: 1
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| Document type: | Journal article |
| Source: | Colloquium Mathematicum; v. N/A, p. 13-pg., 2022-11-14. |
| Abstract | |
We investigate the geometry of C(K, X) and too(X) spaces through complemented subspaces of the form ((R) i,Gamma Xi)c0. For Banach spaces X and Y, we prove that if too(X) has a complemented subspace isomorphic to c0(Y ), then, for some n is an element of N, Xn has a subspace isomorphic to c0(Y ). If K and L are Hausdorff compact spaces and X and Y are Banach spaces having no subspace isomorphic to c0 we further prove the following: (1) If C(K) similar to c0(C(K)) and C(L) similar to c0(C(L)) and too(C(K, X)) similar to too(C(L, Y )), then K and L have the same cardinality. (2) If K and L are infinite and metrizable and too(C(K, X)) similar to too(C(L, Y )), then C(K) is isomorphic to C(L). (AU) | |
| FAPESP's process: | 16/25574-8 - Geometry of Banach Spaces |
| Grantee: | Valentin Raphael Henri Ferenczi |
| Support Opportunities: | Research Projects - Thematic Grants |