On p-Compact Sets in Classical Banach Spaces
نویسندگان
چکیده
Given p ≥ 1, we denote by Cp the class of all Banach spaces X satisfying the equality Kp(Y,X) = Πp(Y,X) for every Banach space Y , Kp (respectively, Πp) being the operator ideal of p-compact operators (respectively, of operators with p-summing adjoint). If X belongs to Cp, a bounded set A ⊂ X is relatively p-compact if and only if the evaluation map U∗ A : X ∗ −→ ∞(A) is p-summing. We obtain p-compactness criteria valid for Banach spaces in Cp. Mathematics Subject Classification: 46B50, 47B07, 47B10
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