THE ALTERNATIVE DUNFORD-PETTIS PROPERTY IN SUBSPACES OF OPERATOR IDEALS
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초록
For several Banach spaces X and Y and operator ideal U, if U(X, Y) denotes the component of operator ideal U; according to Freedman’s definitions, it is shown that a necessary and sufficient condition for a closed subspace M of U(X, Y) to have the alternative Dunford-Pettis property is that all evaluation operators φx :M→Y and Ψy* :M→X*are DP1 operators, where φx(T) = Tx and Ψy* (T) = T*y* for x ∈ X,y* ∈ Y * and T ∈M.
Abstract
For several Banach spaces X and Y and operator ideal U, if U(X, Y) denotes the component of operator ideal U; according to Freedman’s definitions, it is shown that a necessary and sufficient condition for a closed subspace M of U(X, Y) to have the alternative Dunford-Pettis property is that all evaluation operators φx :M→Y and Ψy* :M→X*are DP1 operators, where φx(T) = Tx and Ψy* (T) = T*y* for x ∈ X,y* ∈ Y * and T ∈M.
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