Factorization and extension of positive homogeneous polynomials

Andreas Defant, and Mieczysław Mastyło. "Factorization and extension of positive homogeneous polynomials." Studia Mathematica 221.1 (2014): 87-99. <http://eudml.org/doc/285797>.

@article{AndreasDefant2014,
abstract = {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.},
author = {Andreas Defant, Mieczysław Mastyło},
journal = {Studia Mathematica},
keywords = {factorization; extension; multilinear operators; polynomials; Banach lattice},
language = {eng},
number = {1},
pages = {87-99},
title = {Factorization and extension of positive homogeneous polynomials},
url = {http://eudml.org/doc/285797},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Andreas Defant
AU - Mieczysław Mastyło
TI - Factorization and extension of positive homogeneous polynomials
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 1
SP - 87
EP - 99
AB - 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.
LA - eng
KW - factorization; extension; multilinear operators; polynomials; Banach lattice
UR - http://eudml.org/doc/285797
ER -