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A bilinear version of Orlicz-Pettis theorem
Given three Banach spaces X, Y and Z and a bounded bilinear map B : X×Y → Z, a sequence x = (xn)n ⊆ X is called B-absolutely summable if ∑∞ n=1 ‖B(xn, y)‖Z < ∞ for any y ∈ Y . Connections of this space with `weak(X) are presented. A sequence x = (xn)n ⊆ X is called B-unconditionally summable if ∑∞ n=1 |〈B(xn, y), z∗〉| < ∞ Preprint submitted to Elsevier 21 December 2007 for any y ∈ Y and z∗ ∈ Z∗...
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In 1998, it was proved by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same time measurability of the hypotheses is a necessary condition for learnabil...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1994
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700009618