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On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm

  Published:2003-02-01
 Printed: Feb 2003
  • Yaqiang Yan
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Abstract

Let $l^{\Phi}$ and $L^\Phi (\Omega)$ be the Orlicz sequence space and function space generated by $N$-function $\Phi(u)$ with Orlicz norm. We give equivalent expressions for the nonsquare constants $C_J (l^\Phi)$, $C_J \bigl( L^\Phi (\Omega) \bigr)$ in sense of James and $C_S (l^\Phi)$, $C_S \bigl( L^\Phi(\Omega) \bigr)$ in sense of Sch\"affer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces $l^{\Phi}$ and $L^\Phi (\Omega)$.
Keywords: James nonsquare constant, Schäffer nonsquare constant, Orlicz sequence space, Orlicz function space James nonsquare constant, Schäffer nonsquare constant, Orlicz sequence space, Orlicz function space
MSC Classifications: 46E30 show english descriptions Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
 

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