Arens regularity of some bilinear maps

M. Eshaghi Gordji


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.

Palabras clave

Banach algebra ; Bilinear map ; Arens products.

Texto completo:



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