Autor(es)

Castillo, Jesus M. F. ; Ferenczi, Valentin ; Gonzalez, Manuel

• Tipo de documento: Artigo Científico
• Fonte: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 369, n. 7, p. 38-pg., 2017-07-01.

Resumo

We present new methods to obtain singular twisted sums X circle plus X-Omega (i.e., exact sequence 0 -> X -> X circle plus(Omega) X -> X -> 0 in which the quotient map is strictly singular) when X is an interpolation space arising from a complex interpolation scheme and Omega is the induced centralizer. Although our methods are quite general, we are mainly concerned with the choice of X as either a Hilbert space or Ferenczi's uniformly convex Hereditarily Indecomposable space. In the first case, we construct new singular twisted Hilbert spaces (which includes the only known example so far: the Kalton-Peck space Z(2)). In the second case we obtain the first example of an H.I. twisted sum of an H.I. space. During our study of singularity we introduce the notion of a disjointly singular twisted sum of Kothe function spaces and construct several examples involving reflexive p-convex Kothe function spaces (which includes the function space version of the Kalton-Peck space Z(2)). We then use Rochberg's description of iterated twisted sums to show that there is a sequence F-n of H.I. spaces so that Fm+n is a singular twisted sum of F-m and F-n, while for l > n the direct sum F-n circle plus Fl+m is a nontrivial twisted sum of F-l and Fm+n. (AU)

• Processo FAPESP: 13/11390-4 - Somas torcidas, posições, e teoria de Ramsey em espaços de Banach
• Beneficiário: Valentin Raphael Henri Ferenczi
• Modalidade de apoio: Auxílio à Pesquisa - Regular