Unconditionality for m-homogeneous polynomials on $\ell {ⁿ}_{\infty }$

Andreas Defant, and Pablo Sevilla-Peris. "Unconditionality for m-homogeneous polynomials on $ℓⁿ_{∞}$." Studia Mathematica 232.1 (2016): 45-55. <http://eudml.org/doc/286213>.

@article{AndreasDefant2016,
abstract = {Let χ(m,n) be the unconditional basis constant of the monomial basis $z^\{α\}$, α ∈ ℕ₀ⁿ with |α| = m, of the Banach space of all m-homogeneous polynomials in n complex variables, endowed with the supremum norm on the n-dimensional unit polydisc ⁿ. We prove that the quotient of $sup_\{m\} \@root m \of \{sup_\{m\} χ(m,n)\}$ and √(n/log n) tends to 1 as n → ∞. This reflects a quite precise dependence of χ(m,n) on the degree m of the polynomials and their number n of variables. Moreover, we give an analogous formula for m-linear forms, a reformulation of our results in terms of tensor products, and as an application a solution for a problem on Bohr radii.},
author = {Andreas Defant, Pablo Sevilla-Peris},
journal = {Studia Mathematica},
keywords = {unconditional basis constant; homogeneous polynomials},
language = {eng},
number = {1},
pages = {45-55},
title = {Unconditionality for m-homogeneous polynomials on $ℓⁿ_\{∞\}$},
url = {http://eudml.org/doc/286213},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Andreas Defant
AU - Pablo Sevilla-Peris
TI - Unconditionality for m-homogeneous polynomials on $ℓⁿ_{∞}$
JO - Studia Mathematica
PY - 2016
VL - 232
IS - 1
SP - 45
EP - 55
AB - Let χ(m,n) be the unconditional basis constant of the monomial basis $z^{α}$, α ∈ ℕ₀ⁿ with |α| = m, of the Banach space of all m-homogeneous polynomials in n complex variables, endowed with the supremum norm on the n-dimensional unit polydisc ⁿ. We prove that the quotient of $sup_{m} \@root m \of {sup_{m} χ(m,n)}$ and √(n/log n) tends to 1 as n → ∞. This reflects a quite precise dependence of χ(m,n) on the degree m of the polynomials and their number n of variables. Moreover, we give an analogous formula for m-linear forms, a reformulation of our results in terms of tensor products, and as an application a solution for a problem on Bohr radii.
LA - eng
KW - unconditional basis constant; homogeneous polynomials
UR - http://eudml.org/doc/286213
ER -