Banach Journal of Mathematical Analysis

Strong Arens irregularity of bilinear mappings and reflexivity

Hamid Reza Ebrahimi Vishki and Ali Akbar Khadem-Maboudi

Full-text: Open access

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.

Article information

Source
Banach J. Math. Anal., Volume 6, Number 1 (2012), 155-160.

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1337014674

Digital Object Identifier
doi:10.15352/bjma/1337014674

Mathematical Reviews number (MathSciNet)
MR2862552

Zentralblatt MATH identifier
1252.46040

Subjects
Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 47A07: Forms (bilinear, sesquilinear, multilinear)

Keywords
Arens product bilinear map second dual topological center Banach module action

Citation

Khadem-Maboudi, Ali Akbar; Ebrahimi Vishki, Hamid Reza. Strong Arens irregularity of bilinear mappings and reflexivity. Banach J. Math. Anal. 6 (2012), no. 1, 155--160. doi:10.15352/bjma/1337014674. https://projecteuclid.org/euclid.bjma/1337014674


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