### Abstract

We give a necessary and sufficient condition for the uniformly non- l(Formula presented.) property of Musielak-Orlicz sequence spaces l^{Φ} generated by a sequence Φ=(ϕ_{n}:n⩾l) of finite Orlicz functions such that(Formula presented.) for each n∈ℕ. As a result, for n_{0}⩾2, there exist spaces l^{Φ} which are only uniformly non- l(Formula presented.)for n⩾n_{0}. Moreover we obtain a characterization of uniformly non- l(Formula presented.) and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non- l(Formula presented.) Nakano sequence spaces. This extends a result of Luxemburg in [19].

Original language | English (US) |
---|---|

Pages (from-to) | 71-86 |

Number of pages | 16 |

Journal | Proceedings of the Indian Academy of Sciences - Mathematical Sciences |

Volume | 101 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1991 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Indian Academy of Sciences - Mathematical Sciences*,

*101*(2), 71-86. https://doi.org/10.1007/BF02868018

}

*Proceedings of the Indian Academy of Sciences - Mathematical Sciences*, vol. 101, no. 2, pp. 71-86. https://doi.org/10.1007/BF02868018

**Uniformly non- l(Formula presented.) Musielak-Orlicz sequence spaces.** / Denker, Manfred Heinz; Hudzik, Henryk.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Uniformly non- l(Formula presented.) Musielak-Orlicz sequence spaces

AU - Denker, Manfred Heinz

AU - Hudzik, Henryk

PY - 1991/1/1

Y1 - 1991/1/1

N2 - We give a necessary and sufficient condition for the uniformly non- l(Formula presented.) property of Musielak-Orlicz sequence spaces lΦ generated by a sequence Φ=(ϕn:n⩾l) of finite Orlicz functions such that(Formula presented.) for each n∈ℕ. As a result, for n0⩾2, there exist spaces lΦ which are only uniformly non- l(Formula presented.)for n⩾n0. Moreover we obtain a characterization of uniformly non- l(Formula presented.) and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non- l(Formula presented.) Nakano sequence spaces. This extends a result of Luxemburg in [19].

AB - We give a necessary and sufficient condition for the uniformly non- l(Formula presented.) property of Musielak-Orlicz sequence spaces lΦ generated by a sequence Φ=(ϕn:n⩾l) of finite Orlicz functions such that(Formula presented.) for each n∈ℕ. As a result, for n0⩾2, there exist spaces lΦ which are only uniformly non- l(Formula presented.)for n⩾n0. Moreover we obtain a characterization of uniformly non- l(Formula presented.) and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non- l(Formula presented.) Nakano sequence spaces. This extends a result of Luxemburg in [19].

UR - http://www.scopus.com/inward/record.url?scp=52449147839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449147839&partnerID=8YFLogxK

U2 - 10.1007/BF02868018

DO - 10.1007/BF02868018

M3 - Article

AN - SCOPUS:52449147839

VL - 101

SP - 71

EP - 86

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

SN - 0253-4142

IS - 2

ER -