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BanachJ.Math.Anal.6(2012),no.1,155–160 STRONGARENSIRREGULARITYOFBILINEARMAPPINGSANDREFLEXIVITY B J M A

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Banach J. Math. Anal. 6 (2012), no. 1, 155–160

B

anach

J

ournal of

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athematical

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nalysis ISSN: 1735-8787 (electronic)

www.emis.de/journals/BJMA/

STRONG ARENS IRREGULARITY OF BILINEAR MAPPINGS AND REFLEXIVITY

ALI AKBAR KHADEM-MABOUDI1∗AND HAMID REZA EBRAHIMI VISHKI2 Communicated by M. Abel

Abstract. We provide a sufficient condition for strong (Arens) irregularity of certain bounded bilinear maps, which applies in particular to the adjoint of Banach module actions. We then apply our result to improve several known results concerning to the relation between Arens regularity of certain Banach module actions and reflexivity.

1Department of Biostatistics, Faculty of Paramedical sciences, Shahid Be- heshti University of Medical sciences, Tehran, Iran.

E-mail address: maboudi−[email protected]

2 Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.

E-mail address: [email protected]

Date: Received: 19 October 2011; Accepted: 21 November 2011.

∗ Corresponding author.

2010Mathematics Subject Classification. Primary 46H25; Secondary 47A07.

Key words and phrases. Arens product, bilinear map, second dual, topological center, Banach module action.

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