Annals of Functional Analysis

Uniform openness of multiplication in Orlicz spaces

Ibrahim Akbarbaglu, Saeid Maghsoudi, and Iraj Rahmani

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

multiplication Orlicz space uniformly open mapping normed Riesz space


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.

Export citation


  • [1] I. Akbarbaglu and S. Maghsoudi, Large structures in certain subsets of Orlicz spaces, Linear Algebra Appl. 438 (2013), no. 11, 4363–4373.
  • [2] C. D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, 2nd ed., Math. Surveys Monogr. 105, Amer. Math. Soc., Providence, RI, 2003.
  • [3] M. Balcerzak, A. Majchrzycki, and F. Strobin, Uniformly openness of multiplication in Banach spaces $L_{p}$, preprint.
  • [4] M. Balcerzak, A. Majchrzycki, and A. Wachowicz, Openness of multiplication in some function spaces, Taiwanese J. Math. 17 (2013), no. 3, 1115–1126.
  • [5] M. Balcerzak, F. Strobin, and A. Wachowicz, “Bilinear mappings: selected properties and problems” in Traditional and Present-Day Topics in Real Analysis, Univ. of Łódź Press, Łódź, 2013.
  • [6] M. Balcerzak, A. Wachowicz, and W. Wilczyński, Multiplying balls in the space of continuous functions on $[0,1]$, Studia Math. 170 (2005), no. 2, 203–209.
  • [7] A. Komisarski, A connection between multiplication in $C(X)$ and the dimension of $X$, Fund. Math. 189 (2006), no. 2, 149–154.
  • [8] S. Kowalczyk, On operations in $C(X)$ determined by continuous functions, Acta Math. Hungar. 142 (2014), no. 1, 56–71.
  • [9] M. A. Krasnosel’skii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
  • [10] R. Li, S. Zhong, and C. Swartz, An open mapping theorem without continuity and linearity, Topology Appl. 157 (2010), no. 13, 2086–2093.
  • [11] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, Berlin, 1983.
  • [12] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Pure Appl. Math. 146, Dekker, New York, 1991.
  • [13] A. Wachowicz, Multiplying balls in $C^{(N)}[0,1]$, Real Anal. Exchange 34 (2009), no. 2, 445–450.
  • [14] A. C. Zaanen, Riesz Spaces, II, North-Holland Math. Library 30, North-Holland, Amsterdam, 1983.