Homogeneous Banach spaces on the unit circle

• Autores: Thomas Vils Pedersen
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 44, Nº 1, 2000, págs. 135-155
• Idioma: inglés
• DOI: 10.5565/publmat_44100_04
• Títulos paralelos:
  • Espacios de Banach homogéneos en el círculo unidad
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• Resumen

  • We prove that a homogeneous Banach space ${\mathcal B}$ on the unit circle ${\mathbb T}$ can be embedded as a closed subspace of a dual space $\Xi_{{\mathcal B}}^{\ast}$ contained in the space of bounded Borel measures on ${\mathbb T}$ in such a way that the map ${\mathcal B}\mapsto\Xi_{{\mathcal B}}^{\ast}$ defines a bijective correspondence between the class of homogeneous Banach spaces on ${\mathbb T}$ and the class of prehomogeneous Banach spaces on ${\mathbb T}$.

    We apply our results to show that the