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Abstract Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E) be the space of all E-valued bounded continuous functions on X, equipped… Click to show full abstract
Abstract Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E) be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study dominated and absolutely summing operators T : Cb(X, E) → F . We derive that if X is a locally compact Hausdorff space and E has the Dunford-Pettis property, then every dominated operator T : Cb(X, E) → F is weak Dunford-Pettis. It is shown that every absolutely summing operator T : Cb(X, E) → F is dominated.
Keywords:
strict topology;
topology;
operators absolutely;
summing operators;
absolutely summing;
dominated operators
Journal Title: Quaestiones Mathematicae
Year Published: 2017
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Journal Title: Quaestiones Mathematicae
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!