2012/06/08 by Paweł Kolwicz, Pawel Kolwicz, Kolwicz, Pawel +5
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1206.1860
41 pages
arxiv created 2012/06/08 · openalex publication_date 2012/06/08 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calderón-Lozanovskii spaces are proved. We investigate assumptions on a Banach ideal space E and three Young functions φ1, φ2 and φ, generating the corresponding Calderón-Lozanovskii spaces Eφ1, Eφ2, Eφ so that the space of multipliers M(Eφ1, Eφ) of all measurable x such that x,y ∈ Eφ for any y ∈ Eφ1 can be identified with Eφ2. Sufficient conditions generalize earlier results by Ando, O'Neil, Zabreiko-Rutickii, Maligranda-Persson and Maligranda-Nakai. There are also necessary conditions on functions for the embedding M(Eφ1, Eφ) ⊂ Eφ2 to be true, which already in the case when E = L1, that is, for Orlicz spaces M(Lφ1, Lφ) ⊂ Lφ2 give a solution of a problem raised in the book [Ma89]. 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 M(Eφ1, Eφ) = Eφ2. There are also several examples of independent interest.