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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