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.
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