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Composition operators in Orlicz spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

Yunan Cui ,
Henryk Hudzik ,
Romesh Kumar  and
Lech Maligranda
Yunan Cui
Affiliation:
Department of Mathematics, Harbin University of Sciences and Technology, 52 Xuefu Road, Nanang. Dist. Harbin, Heilongjiang 150080, P. R. of China e-mail: cuiya@mail.hrbust.edu.cn
Henryk Hudzik
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz UniversityUmultowska 87, 61–614 Poznan, Poland, e-mail: hudzik@amu.edu.pl
Romesh Kumar
Affiliation:
Department of Mathematics University of JammuJammu-180 004, India e-mail: romesh_jammu@yahoo.com
Lech Maligranda
Affiliation:
Department of Mathematics Luleå University of TechnologySE-97187 Luleå, Sweden e-mail: lech@sm.luth.se
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Abstract

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Composition operators Cτ between Orlicz spaces Lϕ (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function ϕ and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.

Keywords

composition operatorsOrlicz spacescompact operatorsinterpolation

MSC classification

Secondary: 47B33: Composition operators 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47B07: Operators defined by compactness properties 46B70: Interpolation between normed linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 2 , April 2004 , pp. 189 - 206
Copyright
Copyright © Australian Mathematical Society 2004

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