Archiv der Mathematik

, Volume 84, Issue 5, pp 421–431

Dominated, diagonal polynomials on ℓp spaces

Authors

    • Dipartimento di Matematica, Facoltà di ScienzeUniversità di Catania
  • Joaquín M. Gutiérrez
    • Departamento de Matemática Aplicada, ETS de Ingenieros IndustrialesUniversidad Politécnica de Madrid
Original Paper

DOI: 10.1007/s00013-005-1194-4

Cite this article as:
Cilia, R. & Gutiérrez, J.M. Arch. Math. (2005) 84: 421. doi:10.1007/s00013-005-1194-4

Abstract.

We show that the r-dominated polynomials on ℓp(2 ≦ p ≦ ∞) are integral on ℓ1, and give examples proving that the converse is not true. We characterize when the 2-homogeneous, diagonal polynomials on ℓp(1 < p ≦ ∞) are r-dominated. We prove that, unlike the linear case, there are nuclear polynomials which are not 1-dominated.

Mathematics Subject Classification (2000).

Primary 46G25Secondary 47H60

Copyright information

© Birkhäuser Verlag, Basel 2005