On the projective $LB$-spaces
On the projective $LB$-spaces
The main result of the paper is: An LB-space \(Z\) is projective in the category of all LB-spaces (that is: for every LB-space \(X\) every quotient mapping \(q: X\to Z\) has a right inverse) if and only if \(Z\) is isomorphic to the locally convex direct sum of a sequence of \(\ell_ 1(\Gamma)\)-spaces. The author obtained the same description for projective spaces in the category of all strict LB-spaces. Projective spaces in the category of Banach spaces and of all locally convex spaces were described by \textit{G. Köthe} [Math. Ann. 165, 181-195 (1966; Zbl 0141.116)] and \textit{V. A. Geiler} [Funkts. Anal. Prilozh. 6, No. 2, 79-80 (1972; Zbl 0252.46096)] respectively.
- University of Salento Italy
LB-space, Projective and injective objects in functional analysis, Spaces defined by inductive or projective limits (LB, LF, etc.), description for projective spaces in the category of all strict LB-spaces
LB-space, Projective and injective objects in functional analysis, Spaces defined by inductive or projective limits (LB, LF, etc.), description for projective spaces in the category of all strict LB-spaces
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