Factorization and extension of positive homogeneous polynomials

• Autorzy: Andreas Defant , Mieczysław Mastyło
• Języki publikacji: 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.

Kategorie tematyczne

• 47H60: Multilinear and polynomial operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 1
• Strony: 87-99

Daty

wydano

2014

Twórcy

autor

Andreas Defant

• Institut für Mathematik, Carl von Ossietzky Universität, Postfach 2503, D-26111 Oldenburg, Germany

autor

Mieczysław Mastyło

• Faculty of Mathematics and Computer Science, A. Mickiewicz University
• Institute of Mathematics, Polish Academy of Sciences (Poznań branch), Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/sm221-1-5