Archiv der Mathematik

, Volume 83, Issue 4, pp 364–370 | Cite as

Dominated polynomials on \(\mathcal{L}_P \) -spaces

  • Geraldo Botelho
  • Daniel M. Pellegrino
Original Paper


It is well known that continuous bilinear forms on C(K) ×  C(K) are 2-dominated. This paper shows that generalizations of this result are not to be expected. The main result asserts that for every \(\mathcal{L}_P \) -space E(1≦ p ≦∞), every n ≧ 2, every r > 0 and every Banach space F , there exists an n-homogeneous polynomial P : E  →  F such that P is not of type [Π r ], hence P is neither r-dominated nor r-semi-integral (if n  = 2 and p  =  ∞, F is supposed to contain an isomorphic copy of some \(\ell _q \) , 1≦ q   <  ∞).

Mathematics Subject Classification (2000).

Primary: 46G25 Secondary: 47B10 


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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Faculdade de MatemáticaUniv. Federal de UberlândiaUberlândiaBrazil
  2. 2.Departamento de Matemática e EstatísticaUniv. Federal de Campina GrandeCampina GrandeBrazil

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