Compactness of operators acting from a Lorentz sequence space to an Orlicz sequence space

Jelena Ausekle Faculty of Mathematics, Tartu University Eve Oja Faculty of Mathematics, Tartu University

TBD mathscidoc:1701.332894

Arkiv for Matematik, 36, (2), 233-239, 1997.6
Let$X$and$Y$be closed subspaces of the Lorentz sequence space$d(v, p)$and the Orlicz sequence space$l$_{$M$}, respectively. It is proved that every bounded linear operator from$X$to$Y$is compact whenever $$p > \beta _M : = \inf \{ q > 0:\inf \{ M(\lambda t)/M(\lambda )t^q :0< \lambda ,t \leqslant 1\} > 0.$$ As an application, the reflexivity of the space of bounded linear operators acting from$d(v, p)$to$l$_{$M$}is characterized.
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@inproceedings{jelena1997compactness,
  title={Compactness of operators acting from a Lorentz sequence space to an Orlicz sequence space},
  author={Jelena Ausekle, and Eve Oja},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203553374255703},
  booktitle={Arkiv for Matematik},
  volume={36},
  number={2},
  pages={233-239},
  year={1997},
}
Jelena Ausekle, and Eve Oja. Compactness of operators acting from a Lorentz sequence space to an Orlicz sequence space. 1997. Vol. 36. In Arkiv for Matematik. pp.233-239. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203553374255703.
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