Unconditionality for m-homogeneous polynomials on $ℓⁿ_{∞}$

• Autorzy: Andreas Defant , Pablo Sevilla-Peris
• Języki publikacji: EN

Abstrakty

EN

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 𝔻ⁿ. We prove that the quotient of $sup_{m} \sqrt[m]{sup_{m} χ(m,n)}$ 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.

Kategorie tematyczne

• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B04: Isometric theory of Banach spaces
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 45-55

Daty

wydano

2016

Twórcy

autor

Andreas Defant

• Institut für Mathematik, Universität Oldenburg, D-26111 Oldenburg, Germany

autor

Pablo Sevilla-Peris

• Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Identyfikatory

DOI

10.4064/sm8386-2-2016