منابع مشابه
Remarks on Three-space Problems for the Approximation Property
In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the bounded compact approximation property, then L∞/X has the bounded compact approximation property. We also show that X∗ has the λ-BCAP with conjugate operators if and only if the pair (X,Y ) has the λ-BCAP for each...
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It is shown that sets of sampling for the Bergman space A2 have the “homogeneous approximation property” (HAP) and that sets with this property are sampling for A 2+E. In addition, previous results concerning the boundary behaviour of sampling sets are improved. ForO<p<oo, the Bergman space AP is the set of functions f analytic in the unit disk D = (2 : 1.~1 < 1) with where dA denotes Lebesgue ...
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We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja’s conjecture. As a consequence, we show that each of the spaces c0 and `1 has a subspace which has the AP but fails to have the strong AP.
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2009
ISSN: 1435-9855
DOI: 10.4171/jems/150