On one-sided strong Arens irregularity

摘要

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 G{mathcal{G}}, we show that the convolution algebras N(L_p(G)){mathcal{N}}(L_{p}({mathcal{G}})) of nuclear operators on L_p(G), p Î (1,¥)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.