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Norm-attaining operators into Lorentz sequence spaces

Published online by Cambridge University Press:  25 March 2009

María D. Acosta
María D. Acosta
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain ([email protected])
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Abstract

We prove that the Lorentz sequence spaces do not have the property B of Lindenstrauss. In fact, for any admissible sequences w, v ∈ c0 \ l1, the set of norm-attaining operators from the Orlicz space hϕ(w) (ϕ is a certain Orlicz function) into d(v, 1) is not dense in the corresponding space of operators. We also characterize the spaces such that the subset of norm-attaining operators from the Marcinkiewicz sequence space into its dual is dense in the space of all bounded and linear operators between them.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 225 - 235
Copyright
Copyright © Royal Society of Edinburgh 2009

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