Extension theorems with the range space not necessarily Dedekind complete


We show that every positive linear operator from a majorizing subspace of a separable Fréchet lattice into a Hausdorff locally solid Riesz space with the Fatou property and the σ interpolation property can be extended. We shall also characterize the extreme points of the convex set of all positive linear extensions of a positive linear operator defined on a vector subspace when the range space is not assumed to be Dedekind complete.

DOI Code: 10.1285/i15900932v26n2p153

Keywords: Locally solid Riesz space; Positive linear operator; Hahn-Banach type theorems; $sigma$-Interpolation property

Classification: 47B60; 47B65; 46A22; 46A40

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