Approximation numbers of composition operators on H p
give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞
Weak compactness and Orlicz spaces
We give new proofs that some Banach spaces have Pełczyński's property (V).
Operator ideal properties of vector measures with finite variation
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...
The canonical injection of the Hardy-Orlicz space into the Bergman-Orlicz space
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .
Strongly compact algebras.
An algebra of bounded linear operators on a Hilbert space is said to be if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras are established. Next, a characterization...
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