Abstract
In this note we study the relationship between the vanishing of Ext1(λ(A), λ(A)) and the existence of a regular basis in the Kothe space λ(A). We construct an example of a nuclear Kothe space λ(A) with no regular basis and such that Ext1(λ(A), λ(A))=0. Then we show that for some classes of Kothe spaces λ(A), the vanishing of Ext1(λ(A), λ(A)) yields a regular basis for λ(A).
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