On the \Ext²-problem for Hilbert spaces

2019/08/18 by Sánchez, Félix Cabello, Castillo, Jesús M. F., Corrêa, Willian H. G. +2
#46B25 #46M18 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1908.06529

Abstract

We show that \Ext²(ℓ₂, ℓ₂)≠ 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 \Ext²(ℓ₁, \K)≠ 0 in the category of quasi Banach spaces which solves the four-space problem for local convexity.

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