DOIAbstract
AbstractLet X and Y be the Alexandroff compactifications of the locally compact spaces X and Y, respectively. Denote by Σ(X×Y) the space of all linear extension operators from C((X×Y)⧹(X×Y)) to C((X×Y)). We prove that X and Y are σ-compact spaces if and only if there exists a T∈Σ(X×Y) with ‖T‖<2 if and only if there exists a Γ∈Σ(X×Y) with ‖Γ‖=1. Assuming the existence of a T∈Σ(X×Y) with ‖T‖<3, it is shown that the pseudocompactness of X and Y is equivalent to the fact that ‖Γ‖⩾2 for every Γ∈Σ(X×Y)
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