On the ${\Ext}^2$-problem for Hilbert spaces

Félix Cabello Sánchez; Jesús M. F. Castillo; Willian H. G. Corrêa; Valentin Ferenczi; Ricardo García

On the ${\Ext}^2$-problem for Hilbert spaces

Functional Analysis 2020-01-03 v2

Authors: Félix Cabello Sánchez , Jesús M. F. Castillo , Willian H. G. Corrêa , Valentin Ferenczi , Ricardo García

Abstract

We show that $\Ext^2(\ell_2, \ell_2)\neq 0$ in the category of Banach spaces. This solves a sharpened version of Palamodov's problem and provides a solution to the second order version of Palais problem. We also show that $\Ext^2(\ell_1, \K)\neq 0$ in the category of quasi Banach spaces which solves the four-space problem for local convexity.

Keywords

banach spaces

Cite

@article{arxiv.1908.06529,
  title  = {On the ${\Ext}^2$-problem for Hilbert spaces},
  author = {Félix Cabello Sánchez and Jesús M. F. Castillo and Willian H. G. Corrêa and Valentin Ferenczi and Ricardo García},
  journal= {arXiv preprint arXiv:1908.06529},
  year   = {2020}
}

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