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Article

MORE ON THE ARENS REGULARITY OF $B(X)$

  • R. FAAL (a1) and H. R. EBRAHIMI VISHKI (a2)
Abstract

We focus on a question raised by Daws [‘Arens regularity of the algebra of operators on a Banach space’, Bull. Lond. Math. Soc. 36 (2004), 493–503] concerning the Arens regularity of $B(X)$ , the algebra of operators on a Banach space $X$ . Among other things, we show that $B(X)$ is Arens regular if and only if $X$ is ultrareflexive.

Copyright
© 2016 Australian Mathematical Publishing Association Inc. 
Corresponding author
✉ vishki@um.ac.ir
References
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[1] Arens, R., ‘The adjoint of a bilinear operation’, Proc. Amer. Math. Soc. 2 (1951), 839–848.
[2] Civin, P. and Yood, B., ‘The second conjugate space of a Banach algebra as an algebra’, Pacific J. Math. 11 (1961), 847–870.
[3] Dales, H. G., Banach Algebras and Automatic Continuity (Clarendon Press, Oxford, 2000).
[4] Davis, W. J., Figiel, T., Johnson, W. B. and Pełczyński, A., ‘Factoring weakly compact operators’, J. Funct. Anal. 17 (1974), 311–327.
[5] Daws, M., ‘Arens regularity of the algebra of operators on a Banach space’, Bull. Lond. Math. Soc. 36 (2004), 493–503.
[6] Heinrich, S., ‘Ultraproducts in Banach space theory’, J. reine angew. Math. 313 (1980), 72–104.
[7] Young, N. J., ‘Periodicity of functionals and representations of normed algebras on reflexive spaces’, Proc. Edinb. Math. Soc. (2) 20 (1976–77), 99–120.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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