کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6415212 | 1334972 | 2014 | 44 صفحه PDF | دانلود رایگان |
The well-known factorization theorem of LozanovskiÄ may be written in the form L1â¡EâEâ², where â means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the question when one can factorize F through E, i.e., when Fâ¡EâM(E,F), where M(E,F) is the space of pointwise multipliers from E to F. Properties of M(E,F) were investigated in our earlier paper [41] and here we collect and prove some properties of the construction EâF. The formulas for pointwise product of Calderón-LozanovskiÄ EÏ-spaces, Lorentz spaces and Marcinkiewicz spaces are proved. These results are then used to prove factorization theorems for such spaces. Finally, it is proved in Theorem 11 that under some natural assumptions, a rearrangement invariant Banach function space may be factorized through a Marcinkiewicz space.
Journal: Journal of Functional Analysis - Volume 266, Issue 2, 15 January 2014, Pages 616-659