This is an announcement for the paper "Pointwise multipliers of Calder'on-Lozanovskii spaces" by Pawel Kolwicz, Karol Lesnik, and Lech Maligranda.
Abstract: Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calder'on-Lozanovskii spaces are proved. We investigate assumptions on a Banach ideal space E and three Young functions \varphi_1, \varphi_2 and \varphi, generating the corresponding Calder'on-Lozanovskii spaces E_{\varphi_1}, E_{\varphi_2}, E_{\varphi} so that the space of multipliers M(E_{\varphi_1}, E_{\varphi}) of all measurable x such that x,y \in E_{\varphi} for any y \in E_{\varphi_1} can be identified with E_{\varphi_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_{\varphi_1}, E_{\varphi}) \subset E_{\varphi_2} to be true, which already in the case when E = L^1, that is, for Orlicz spaces M(L^{\varphi_1}, L^{\varphi}) \subset L^{\varphi_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 \varphi_2 such that M(E_{\varphi_1}, E_{\varphi}) = E_{\varphi_2}. There are also several examples of independent interest.
Archive classification: math.FA
Mathematics Subject Classification: Functional Analysis (math.FA)
Remarks: 41 pages
Submitted from: lech.maligranda@ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1860
or