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Projections from L ( X , Y ) onto K ( X , Y )

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let X and Y be Banach spaces such that X is weakly compactly generated Asplund space and X * has the approximation property (respectively Y is weakly compactly generated Asplund space and Y * has the approximation property). Suppose that L ( X , Y ) K ( X , Y ) and let 1 < λ < 2 . Then X (respectively Y ) can be equivalently renormed so that any projection P of L ( X , Y ) onto K ( X , Y ) has the sup-norm greater or equal to λ .

Projections on Hardy spaces in the Lie ball.

David Bekollé (1994)

Publicacions Matemàtiques

On the Lie ball w of Cn, n ≥ 3, we prove that for all p ∈ [1,∞), p ≠ 2, the Hardy space Hp(w) is an uncomplemented subspace of the Lebesgue space Lp(∂0w, dσ), where ∂0w denotes the Shilov boundary of w and dσ is a normalized invariant measure of ∂0w.

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