Archiv der Mathematik

, Volume 84, Issue 5, pp 421–431

Dominated, diagonal polynomials on ℓp spaces

Original Paper

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 46G25 Secondary 47H60 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Facoltà di ScienzeUniversità di CataniaCataniaItaly
  2. 2.Departamento de Matemática Aplicada, ETS de Ingenieros IndustrialesUniversidad Politécnica de MadridMadridSpain

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