On essentially incomparable Banach spaces

• Autores: Miguel González Velasco
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 6, Nº 2-3, 1991, págs. 135-138
• Idioma: inglés
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• Resumen

  • We introduce the concept of essentially incomparable Banach spaces, and give some examples. Then, for two essentially incomparable Banach spaces X and Y, we prove that a complemented subspace of the product X x Y is isomorphic to the product of a complemented subspace of X and a complemented subspace of Y. If, additionally, X and Y are isomorphic to their respective hyperplanes, then the group of invertible operators in X x Y is not connected. The results can be applied to some classical Banach spaces.