Automorphisms of $\mathcal{C}(K)$ -spaces and extension of linear operators
Kalton, N. J.
Illinois J. Math., Tome 52 (2008) no. 1, p. 279-317 / Harvested from Project Euclid
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We study the class of separable (real) Banach spaces X which can be embedded into a space $\mathcal{C}(K)$ (K compact metric) in only one way up to automorphism. We show that in addition to the known spaces c0 (and all it subspaces) and ℓ1 (and all its weak*-closed subspaces) the space c0(ℓ1) has this property. We show on the other hand (answering a question of Castillo and Moreno) that ℓp for 1p can be embedded in a super-reflexive space X so that there is an operator $T\dvtx\ell_{p}\to\mathcal{C}(K)$ which has no extension, answering a question of Zippin.
Publié le : 2008-05-15
Classification:  46B03,  46B20 
@article{1242414132,
     author = {Kalton, N. J.},
     title = {Automorphisms of $\mathcal{C}(K)$ -spaces and extension of linear operators},
     journal = {Illinois J. Math.},
     volume = {52},
     number = {1},
     year = {2008},
     pages = { 279-317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1242414132}
}

Kalton, N. J. Automorphisms of $\mathcal{C}(K)$ -spaces and extension of linear operators. Illinois J. Math., Tome 52 (2008) no. 1, pp.  279-317. http://gdmltest.u-ga.fr/item/1242414132/