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Proyecciones (Antofagasta)

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Abstract

GORDJI, M. ESHAGHI. ARENS REGULARITY OF SOME BILINEAR MAPS. Proyecciones (Antofagasta) [online]. 2009, vol.28, n.1, pp.21-26. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172009000100002.

Let H be a Hilbert space. we show that the following statements are equivalent: (a) B(H) is finite dimension, (b) every left Banach module action l : B(H)×H → H, is Arens regular (c) every bilinear map f : B(H)*→ B(H) is Arens regular. Indeed we show that a Banach space X is reflexive if and only if every bilinear map f : X* × X → X* is Arens regular.

Keywords : Banach algebra; Bilinear map; Arens products.

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