For a locally compact group G and p ∈ (1, ∞), we study X(Lp(G)), the G-continuous operators on Lp(G), and the Banach algebra X(Lp(G))∗. We use a representation of the latter to show that, for infinite discrete groups G, the left topological centre condition on the convolution algebra N(ℓp(G)) of nuclear operators is equivalent to a commutation relation. Then, using an automatic normality result inspired by [16], we give a two-point left dtc set for N(ℓp(G)) in the case where G is abelian, and a two-point right dtc set for N(ℓp(G)) using results from [9].

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Keywords Arens products, Nuclear operators, Topological centers
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Journal Indiana University Mathematics Journal
Mazowita, M. (Matthew), & Neufang, M. (2017). G-continuous operators and dtc sets for the convolution algebra of nuclear operators. Indiana University Mathematics Journal, 66(1), 161–181. doi:10.1512/iumj.2017.66.5775