Interpolation, twisted sums and borelian classes of Banach Spaces
Homological and descriptive set theory methods in Banach spaces
Applications of Functional Analysis to Quantum Information Theory
| Full text | |
| Author(s): |
Castillo, Jesus M. F.
;
Ferenczi, Valentin
;
Gonzalez, Manuel
Total Authors: 3
|
| Document type: | Journal article |
| Source: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 369, n. 7, p. 38-pg., 2017-07-01. |
| Abstract | |
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) | |
| FAPESP's process: | 13/11390-4 - Twisted sums, positions and Ramsey theory in Banach Spaces |
| Grantee: | Valentin Raphael Henri Ferenczi |
| Support Opportunities: | Regular Research Grants |