Pointwise multipliers of Calderón-Lozanovskiǐ spaces

Authors

  • Paweł Kolwicz,

    1. Institute of Mathematics of Electric Faculty, Poznań University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland. Phone: +48 61 6652802, Fax: +48 61 6652348
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  • Karol Leśnik,

    1. Institute of Mathematics of Electric Faculty, Poznań University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland. Phone: +48 61 6652802, Fax: +48 61 6652348
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  • Lech Maligranda

    Corresponding author
    1. Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden. Phone: +48 61 6652359, Fax: +48 61 6652348
    • Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden. Phone: +46 920 491318, Fax: +46 920 491073
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Abstract

Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calderón-Lozanovskiǐ spaces are proved. We investigate assumptions on a Banach ideal space E and three Young functions φ1, φ2 and φ, generating the corresponding Calderón-Lozanovskiǐ spaces equation image so that the space of multipliers equation image of all measurable x such that xyEφ for any equation image can be identified with equation image. Sufficient conditions generalize earlier results by Ando, O'Neil, Zabreǐko-Rutickiǐ, Maligranda-Persson and Maligranda-Nakai. There are also necessary conditions on functions for the embedding equation image to be true, which already in the case when E = L1, that is, for Orlicz spaces equation image give a solution of a problem raised in the book 26. Some properties of a generalized complementary operation on Young functions, defined by Ando, are investigated in order to show how to construct the function φ2 such that equation image. There are also several examples of independent interest.

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