Bulletin of the Australian Mathematical Society

Research Article

A counterexample using 4-linear forms

David Pérez-Garcíaa1

a1 Área de Matemática Aplicada, Departmento de Matemáticas y Física Aplicadas y, Ciencias de la Naturaleza, Escuela Superior de Ciencias Experimentales y Tecnología, Universidad Rey Juan Carlos, Edificio Departmental II, 28933 Móstoles (Madrid), e-mail: dperezg@escet.urjc.es

We prove that, for n ≥ 4 and arbitrary infinite dimensional Banach spaces X1,…Xn, there exists an extendible n-linear form T: X1 x…x Xn →  that is not integral.

(Received June 21 2004)