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Normal structure and weakly normal structure of Orlicz sequence spaces

Normal structure and weakly normal structure of Orlicz sequence spaces

For a convex Orlicz function<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi colon bold upper R Subscript plus Baseline right-arrow bold upper R Subscript plus Baseline union StartSet normal infinity EndSet"><mml:semantics><mml:mrow><mml:mi>φ<!-- φ --></mml:mi><mml:mo>:</mml:mo><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="bold">R</mml:mi></mml:mrow></mml:mrow><mml:mo>+</mml:mo></mml:msub></mml:mrow><mml:mo stretchy="false">→<!-- → --></mml:mo><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="bold">R</mml:mi></mml:mrow></mml:mrow><mml:mo>+</mml:mo></mml:msub></mml:mrow><mml:mo>∪<!-- ∪ --></mml:mo><mml:mo fence="false" stretchy="false">{</mml:mo><mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi><mml:mo fence="false" stretchy="false">}</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">\varphi …