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1
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Weak compactness and Orlicz spaces

100%
Lefèvre P., Li D., Queffélec H., Rodríguez-Piazza L.
Colloquium Mathematicum
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2008
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tom 112
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nr 1
23-32
EN
We give new proofs that some Banach spaces have Pełczyński's property (V).
2
Content available remote

Approximation numbers of composition operators on Hp

100%
Li D., Queffélec H., Rodríguez-Piazza L.
Concrete Operators
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2015
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tom 2
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nr 1
EN
give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞
3
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The canonical injection of the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $𝔅^{Ψ}$

100%
Lefèvre P., Li D., Queffélec H., Rodríguez-Piazza L.
Studia Mathematica
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2011
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tom 202
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nr 2
123-144
EN
We study the canonical injection from the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $𝔅^{Ψ}$.
4
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Operator ideal properties of vector measures with finite variation

100%
Okada S., Ricker W., Rodríguez-Piazza L.
Studia Mathematica
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2011
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tom 205
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nr 3
215-249
EN
Given a vector measure m with values in a Banach space X, a desirable property (when available) of the associated Banach function space L¹(m) of all m-integrable functions is that L¹(m) = L¹(|m|), where |m| is the [0,∞]-valued variation measure of m. Closely connected to m is its X-valued integration map Iₘ: f ↦ ∫f dm for f ∈ L¹(m). Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property L¹(m) = L¹(|m|) and the membership of Iₘ in various classical operator ideals(e.g., the compact, p-summing, completely continuous operators). Depending on which operator ideal is under consideration, the geometric nature of the Banach space X may also play a crucial role. Of particular importance in this regard is whether or not X contains an isomorphic copy of the classical sequence space ℓ¹. The compact range property of X is also relevant.
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