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A lifting theorem for locally convex subspaces of \(L_ 0\). (English) Zbl 0829.46054

Summary: We prove that for every closed locally convex subspace \(E\) of \(L_0\) and for any continuous linear operator \(T\) from \(L_0\) to \(L_0/E\) there is a continuous linear operator \(S\) from \(L_0\) to \(L_0\) such that \(T= QS\) where \(Q\) is the quotient map from \(L_0\) to \(L_0/E\).

MSC:

46M10 Projective and injective objects in functional analysis
46G15 Functional analytic lifting theory
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

lifting theorem
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