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Monotone extenders for bounded c-valued functions

Kaori Yamazaki (2010)

Studia Mathematica

Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, C ( A , c ) the set of all bounded continuous functions f: A → c, and C A ( X , c ) the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender u : C ( A , c ) C A ( X , c ) . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...

M-weak and L-weak compactness of b-weakly compact operators

J. H'Michane, A. El Kaddouri, K. Bouras, M. Moussa (2013)

Commentationes Mathematicae Universitatis Carolinae

We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).

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