The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of <i>c</i><sub>0</sub>

CUI Yun’an; AN Lili

doi:10.3969/j.issn.1000-5641.201911007

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CUI Yun’an, AN Lili. The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c0[J]. Journal of East China Normal University (Natural Sciences), 2020, (2): 35-40. doi: 10.3969/j.issn.1000-5641.201911007

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CUI Yun’an, AN Lili. The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c₀[J]. Journal of East China Normal University (Natural Sciences), 2020, (2): 35-40. doi: 10.3969/j.issn.1000-5641.201911007

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The Orlicz space equipped with the Φ-Amemiya norm contains an order asymptotically isometric copy of c₀

doi: 10.3969/j.issn.1000-5641.201911007

College of Science, Harbin University of Science and Technology, Harbin　150080, China

Received Date: 2019-01-24
Publish Date: 2020-03-01

Abstract

Abstract

In Orlicz space, a new norm that is equivalent to the Luxemburg norm is introduced. It is called the Φ-Amemiya norm: ${\left\| x \right\|_{\Phi ,{\Phi _1}}} = \inf \left\{ {\frac{1}{k}\left( {1 + \Phi \left( {{{ I}_{{\Phi _1}}}\left( {kx} \right)} \right)} \right)} \right\}$. It is shown, furthermore, that the Orlicz function space equipped with this norm $\left\{ {{L_{\Phi ,{\Phi _{\rm{1}}}}},{{\left\| \cdot \right\|}_{\Phi ,{\Phi _1}}}} \right\}$ is a Banach space. Hence, this paper demonstrates the conditions for the Orlicz space with the Φ-Amemiya norm to contain an asymptotically isometric copy of c₀.
- Orlicz space,
- Amemiya norm,
- condition Δ₂,
- order asymptotically isometric copy of c₀

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References(18)

References

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