TY - JOUR AU - Gordji, M. Eshaghi PY - 1970/01/01 Y2 - 2024/03/28 TI - Arens regularity of some bilinear maps JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 28 IS - 1 SE - DO - 10.4067/S0716-09172009000100002 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1381 SP - 21-26 AB - 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. ER -