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Some remarks on thin operators

Published online by Cambridge University Press:  12 July 2007

Julio Flores
Julio Flores
Affiliation:
Area de Matemática Aplicada, Escet, URJC, 28933 Móstoles, Madrid, Spain (j.flores@escet.urjc.es)
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Abstract

We show that if (Ω, Σ, μ) and (Ω′, Σ′, μ′) are probability spaces, then every regular operator T : Lp(μ) → Lq(μ′), 1 < p < ∞, 1 ≤ q < ∞, is thin if and only if it is strictly singular. We also show that if 0 ≤ S ≤ T : Lp(μ) → Lq(μ′), then T thin implies S is thin. We extend these results to some Köthe function spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 2 , April 2004 , pp. 317 - 331
Copyright
Copyright © Royal Society of Edinburgh 2004

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