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On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm
Published online by Cambridge University Press: 20 November 2018
Abstract
Let ${{l}^{\Phi }}$ and ${{L}^{\Phi }}\left( \Omega \right)$ 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 ${{C}_{J}}\left( {{l}^{\Phi }} \right),\,{{C}_{J}}\left( {{L}^{\Phi }}\left( \Omega \right) \right)$ in sense of James and ${{C}_{S}}\left( {{l}^{\Phi }} \right),\,{{C}_{S}}\left( {{L}^{\Phi }}\left( \Omega \right) \right)$ in sense of Schäffer. 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 ${{L}^{\Phi}}\left(\Omega \right)$.
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- Copyright © Canadian Mathematical Society 2003
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