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arXiv · 1206.1860

Pointwise multipliers of Calderón-Lozanovskii spaces

Pawel Kolwicz·Karol Lesnik·Lech Maligranda
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Abstract

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 φ_1, φ_2 and φ, generating the corresponding Calderón-Lozanovskii spaces E_{φ_1}, E_{φ_2}, E_φ so that the space of multipliers M(E_{φ_1}, E_φ) of all measurable x such that x,y \in E_φ for any y \in E_{φ_1} can be identified with E_{φ_2}. 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(E_{φ_1}, E_φ) \subset E_{φ_2} to be true, which already in the case when E = L^1, that is, for Orlicz spaces M(L^{φ_1}, L^φ) \subset L^{φ_2} 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 φ_2 such that M(E_{φ_1}, E_φ) = E_{φ_2}. There are also several examples of independent interest.

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Pawel Kolwicz, Karol Lesnik, Lech Maligranda. 2012-06-08. Pointwise multipliers of Calderón-Lozanovskii spaces. https://arxiv.org/abs/1206.1860

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