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We show that a Banach space X is an ℒ₁-space (respectively, an -space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an -space.
We give sufficient conditions on Banach spaces and so that their projective tensor product , their injective tensor product , or the dual contain complemented copies of .
We give new characterizations of Banach spaces not containing in terms of integral and -dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.
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