$\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm

SHI Zhong-rui; ZHAI Jia-yu

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Jan. 2012

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SHI Zhong-rui, ZHAI Jia-yu. $\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 63-73.

Citation:

SHI Zhong-rui, ZHAI Jia-yu. $\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 63-73.

SHI Zhong-rui, ZHAI Jia-yu. $\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 63-73.

Citation:

SHI Zhong-rui, ZHAI Jia-yu. $\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 63-73.

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$\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm

1.
Department of Mathematics, Shanghai University, Shanghai 200444, China

Received Date: 2011-03-01
Rev Recd Date: 2011-06-01
Publish Date: 2012-01-25

Abstract

Abstract

In this paper, we gave the sufficient and necessary conditions of $\lambda$ point in a generalized Orlicz function space equipped with the Luxemburg norm, by methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between points in the unit balls of classical and that of generalized Orlicz spaces: all of the classical spaces are $\lambda$ points, but some of the generalized spaces are not. Finally, we gave the criteria of the $\lambda$ property and the uniform $\lambda$ property of generalized spaces.
- generalized Orlicz spaces,
- Luxemburg norm,
- $\lambda$ property,
- $\lambda$ points,
- uniform $\lambda$ property

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References(1)

References

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