Let $F$ be a non-archimedean local field of residue characteristic neither 2 nor 3 equipped with a galois involution with fixed field ${{F}_{0}}$, and let $G$ be a symplectic group over $F$ or an unramified unitary group over ${{F}_{0}}$. Following the methods of Bushnell–Kutzko for $\text{GL}(N,F)$, we define an analogue of a simple type attached to a certain skew simple stratum, and realize a type in $G$. In particular, we obtain an irreducible supercuspidal representation of $G$ like $\text{GL}(N,F)$.

In this paper, we investigate projectivity in the category of operator spaces. In particular, we show that the Fourier algebra of a locally compact group $G$ is operator biprojective if and only if $G$ is discrete.

We show that for certain compact right topological groups, $\overline{r(G)}$, the strong operator topology closure of the image of the right regular representation of $G$ in $L(H)$, where $H\,=\,{{L}^{2}}\,(G)$, is a compact topological group and introduce a class of representations, $R$ , which effectively transfers the representation theory of $\overline{r(G)}$ over to $G$. Amongst the groups for which this holds is the class of equicontinuous groups which have been studied by Ruppert in [10].We use familiar examples to illustrate these features of the theory and to provide a counter-example. Finally we remark that every equicontinuous group which is at the same time a Borel group is in fact a topological group.