Skip to main content
×
Home
    • Aa
    • Aa

BANACH SPACES OF CONTINUOUS VECTOR-VALUED FUNCTIONS OF ORDINALS

  • Elói Medina Galego (a1)
Abstract
Abstract

Let $X$ be a Banach space and $\xi$ an ordinal number. We study some isomorphic classifications of the Banach spaces $X^\xi$ of the continuous $X$-valued functions defined in the interval of ordinals $[1,\xi]$ and equipped with the supremum norm. More precisely, first we use the continuum hypothesis to give an isomorphic classification of $C(I)^\xi$, $\xi\geq\omega_1$. Then we present a characterization of the separable Banach spaces $X$ that are isomorphic to $X^\xi$, $\forall\xi$, $\omega\leq\xi lt \omega_1$. Finally, we show that the isomorphic classifications of $(C(I)\oplus F^*)^\xi$ and $\ell_\infty(\N)^\xi$, where $F$ is the space of Figiel and $\omega\leq\xi lt \omega_1$ are similar to that of $\R^\xi$ given by Bessaga and Pelczynski.

AMS 2000 Mathematics subject classification: Primary 46B03; 46B20; 46E15

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords: