On one-sided strong Arens irregularity

Abstract.

We present a natural class of Banach algebras which are one-sided strongly Arens irregular. More precisely, for any non-compact, second countable locally compact group ${\mathcal{G}}$, we show that the convolution algebras ${\mathcal{N}}(L_{p}({\mathcal{G}}))$ of nuclear operators on $L_{p}({\mathcal{G}}), p \in (1,\infty)$, as introduced and studied by the author in [3], [6], are left but not right strongly Arens irregular.