Annals of Functional Analysis

Uniform openness of multiplication in Orlicz spaces

Ibrahim Akbarbaglu, Saeid Maghsoudi, and Iraj Rahmani

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Abstract

Let Φ and Ψ be Young functions, and let LΦ(Ω) and LΨ(Ω) be corresponding Orlicz spaces on a measure space (Ω,μ). Our aim in this paper is to prove that, under mild conditions on Φ and Ψ, the multiplication from LΦ(Ω)×LΨ(Ω) onto L1(Ω) is uniformly open. This generalizes an interesting recent result due to M. Balcerzak, A. Majchrzycki, and F. Strobin in 2013.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 543-551.

Dates
Received: 17 November 2015
Accepted: 14 March 2016
First available in Project Euclid: 31 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1472659940

Digital Object Identifier
doi:10.1215/20088752-3661305

Mathematical Reviews number (MathSciNet)
MR3543146

Zentralblatt MATH identifier
1354.46029

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 47A07: Forms (bilinear, sesquilinear, multilinear) 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 06B30: Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]

Keywords
multiplication Orlicz space uniformly open mapping normed Riesz space

Citation

Akbarbaglu, Ibrahim; Maghsoudi, Saeid; Rahmani, Iraj. Uniform openness of multiplication in Orlicz spaces. Ann. Funct. Anal. 7 (2016), no. 4, 543--551. doi:10.1215/20088752-3661305. https://projecteuclid.org/euclid.afa/1472659940


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References

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