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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.28 no.1 Antofagasta May 2009

http://dx.doi.org/10.4067/S0716-09172009000100002 

Proyecciones Journal of Mathematics
Vol. 28, No 1, pp. 21—26, Mayo 2009.
Universidad Católica del Norte
Antofagasta - Chile


ARENS REGULARITY OF SOME BILINEAR MAPS


M. ESHAGHI GORDJI

Semnan University, Irán.


Correspondencia a:


Abstract
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.


Subjclass [2000] : Primary 46H25, 16E40.
Keywords : Banach algebra, Bilinear map, Arens products.

REFERENCES
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M. ESHAGHI GORDJI
Department of Mathematics
Semnan University
P. O. Box 35195-363
Semnan
Iran
e-mail : maj_ess@yahoo.com

Received : February 2008. Accepted : November 2008

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