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A factorization formula for some entropy ideals

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Cobos, Fernando and Resina, Ivam and Soria, Fernando (1988) A factorization formula for some entropy ideals. Note di Matematica, 8 (1). pp. 57-65. ISSN 1123-2536

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Abstract

The paper deals with the entropy ideals generated by the Lorentz- Marcinkiewicz spaces of the type λ ∞ (ϕ) where ϕ is a function parameter. The entropy ideal generated by λ ∞ (ϕ) is the set of all operators between Banach spaces whose sequence of the entropy numbers belongs to λ ∞ (ϕ). The entropy ideals play an important role in the characterization of the degree of compactness of weakly singular integral operators. As a continuation of F. Cobos' investigation of the entropy ideals of the type λ p (ϕ), the authors prove a factorization formula saying that the entropy ideal corresponding to the product of two function parameters is the product of the entropy ideals corresponding to the factors. The proof uses the interpolation with function parameters and as a by-product, the authors obtain informations on the behaviour of the entropy numbers under the interpolation.


Item Type:Article
Uncontrolled Keywords:Entropy ideals; Lorentz-Marcinkiewicz spaces; operators between Banach spaces; entropy numbers; degree of compactness of weakly singular integral operators
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:23331
Deposited On:04 Nov 2013 16:16
Last Modified:14 Jun 2018 11:09

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