On pairs of Banach spaces which are isomorphic to complemented subspaces of each other

Volume 101 / 2004

Elói Medina Galego Colloquium Mathematicum 101 (2004), 279-287 MSC: Primary 46B03; Secondary 46B20. DOI: 10.4064/cm101-2-10

Abstract

We establish the existence of Banach spaces $E$ and $F$ isomorphic to complemented subspaces of each other but with $E^m \oplus F^n$ isomorphic to $E^p \oplus F^q$, $m, n, p, q \in {\mathbb N}$, if and only if $m=p$ and $n=q$.

Authors

  • Elói Medina GalegoDepartment of Mathematics
    IME, University of São Paulo
    São Paulo, 05508-090, Brazil
    e-mail

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