Rocky Mountain Journal of Mathematics

Uniformly non-square points and representation of functionals of Orlicz-Bochner sequence spaces

Zhongrui Shi and Yu Wang

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In this work, a representation of functionals and a necessary and sufficient condition for uniformly non-square points of Orlicz-Bochner sequence spaces endowed with the Orlicz norm are given.

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Rocky Mountain J. Math., Volume 48, Number 2 (2018), 639-660.

First available in Project Euclid: 4 June 2018

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Primary: 46B20: Geometry and structure of normed linear spaces 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Uniformly non-square point uniformly non-squareness Orlicz-Bochner sequence space representation of functionals


Shi, Zhongrui; Wang, Yu. Uniformly non-square points and representation of functionals of Orlicz-Bochner sequence spaces. Rocky Mountain J. Math. 48 (2018), no. 2, 639--660. doi:10.1216/RMJ-2018-48-2-639.

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  • G. Alherk and H. Hudzik, Uniformly non-$l_{n}^{(1)}$ Musielak-Orlicz spaces of Bochner type, Forum Math. 1 (1989), 403–410.
  • S.T. Chen, Geometry of Orlicz space, Dissert. Math., Warsawa, 1992.
  • S.T. Chen and Y.W. Wang, The definition of normed linear spaces, Chinese Ann. Math. 9 (1988), 330–334.
  • Y. Cui, H. Hudzik, M. Wisła and K. Wlaźlak, Non-squareness properties of Orlicz spaces equipped with the $p$-Amemiya norm, Nonlin. Anal. 75 (2012), 3973–3993.
  • P. Foralewski, H. Hudzik and P. Kolwicz, Non-squareness properties of Orlicz-Lorentz sequence spaces, J. Funct. Anal. 264 (2013), 605–629.
  • J. García-Falset, E. Llorens-Fuster and E.M. Mazcuña-Navarro, Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings, J. Funct. Anal. 233 (2006), 494–514.
  • R. Grz\kaślewicz, H. Hudzik and W. Orlicz, Uniform non-$l_{n}^{1}$ property in some normed spaces, Bull. Pol. Acad. Sci. Math. 34 (1986), 161–171.
  • H. Hudzik, Uniformly non-$l^{1}_{n}$ Orlicz space with Luxemburg norm, Stud. Math. 81 (1985), 271–284.
  • H. Hudzik, Some class of uniformly non-square Orlicz-Bochner spaces, Comment. Math. Univ. Carolin. 26 (1985), 269–274.
  • ––––, Locally uniformly non-$l_{n}^{1}$ Orlicz space, Rend. Circ. Mat. Palermo 10 (1985), 49–56.
  • H. Hudzik, A. Kamińska and W. Kurc, Uniformly non-$l_{n}^{1}$ Musielak-Orlicz spaces, Bull. Pol. Acad. Sci. Math. 35 (1987), 441–448.
  • R.C. James, Uniformly nonsquare Banach spaces, Ann. Math. 80 (1964), 542–550.
  • ––––, Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409–419.
  • A. Kamińska and B. Turett, Uniformly non-$l^{1}(n)$ Orlicz-Bochner space, Bull. Pol. Acad. Sci. Math. 35 (1987), 211–218.
  • M.A. Krasnosel'skiĭ and Y.B. Rutickiĭ, Convex functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961.
  • H.L. Royden, Real analysis, Macmillan, New York, 1988.
  • S.Q. Shang and Y.A. Cui, Uniformly nonsquareness and locally uniform nonsquareness in Orlicz-Bochner function spaces and applications, J. Funct. Anal. 267 (2014), 2056–2076.
  • Z.R. Shi and Y.J. Wang, The nonsquare point of Orlicz-Bochner squence spaces, Southeast Asian Bull. Math. 41 (2017), 249–258.
  • ––––, The locally uniformly non-square points of Orlicz-Bochner sequence spaces, Math. Nachr. 290 (2017), 920–929.
  • K. Sundaresan, Uniformly non-square Orlicz spaces, Nieuw Arch. Wiskd. 14 (1966), 31–39.
  • T.F. Wang, Z.R. Shi and Y.H. Li, On uniformly nonsquare points and nonsquare points of Orlicz spaces, Comment. Math. Univ. Carolin. 33 (1992), 477–484.
  • D.W. Zhang, Nonsquareness of Orlicz-Bochner spaces, Arch. Shanghai University, Shanghai, 2009.