A note on p-limited sets in dual Banach spaces
Monatshefte für Mathematik(2022)
摘要
If A is a bounded subset of X^* and ℓ _∞ (A) is the Banach space (sup norm) of all bounded real-valued functions defined on A, let E: X→ℓ _∞ (A) be the evaluation map defined by Ex(x^*)= x^*(x) , x∈ X , x^*∈ A . We show that a subset A of X^* is a p-limited set if and only if E: X→ℓ _∞ (A) is p-summing. We give a characterization of p-limited sets in X^* using w^* -w operators T:X^*→ℓ _p .
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关键词
p-limited sets,p-summing operators,p-compact sets,The p-Dunford Pettis property,46B20,46B25,46B28
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