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## Studia Mathematica

2014 | 221 | 1 | 87-99
Tytuł artykułu

### Factorization and extension of positive homogeneous polynomials

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EN
Abstrakty
EN
We study the following problem: Given a homogeneous polynomial from a sublattice of a Banach lattice to a Banach lattice, under which additional hypotheses does this polynomial factorize through $L_{p}$-spaces involving multiplication operators? We prove that under some lattice convexity and concavity hypotheses, for polynomials certain vector-valued norm inequalities and weighted norm inequalities are equivalent. We combine these results and prove a factorization theorem for positive homogeneous polynomials which is a variant of a celebrated factorization theorem for linear operators due to Maurey and Rosenthal. Our main application is a Hahn-Banach extension theorem for positive homogeneous polynomials between Banach lattices.
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Tom
Numer
Strony
87-99
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
• Institut für Mathematik, Carl von Ossietzky Universität, Postfach 2503, D-26111 Oldenburg, Germany
autor
• Faculty of Mathematics and Computer Science, A. Mickiewicz University
• Institute of Mathematics, Polish Academy of Sciences (Poznań branch), Umultowska 87, 61-614 Poznań, Poland
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