Linear mapping preserving the kernel or the range of operators

• Autores: Mourad Oudghiri
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 24, Nº 3, 2009, págs. 251-258
• Idioma: inglés
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• Resumen

  • Let X and Y be two in¯nite dimensional real or complex Banach spaces. In this note we determine the forms of surjective additive maps Á : L(X) ! L(Y ) preserving the kernel's dimension or the range's codimension. As consequence, we establish that Á :

    L(X) ! L(X) preserves the kernel (respectively, the range) if and only if there exists an invertible operator A 2 L(X) such that Á(T) = AT (respectively, Á(T) = TA) for all T 2 L(X)