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We investigate quantum group generalizations of various density results from Fourier analysis on compact groups. In particular, we establish the density of characters in the space of fixed points of the conjugation action on $L^2(mathbb{G})$, and use this result to show the weak* density and norm density of characters in $ZL^{infty}(mathbb{G})$ and $ZC(mathbb{G})$, respectively. As a corollary, we partially answer an open question of Woronowicz. At the level of $L^1(mathbb{G})$, we show that the center $mathcal{Z}(L^1(mathbb{G}))$ is precisely the closed linear span of the quantum characters for a large class of compact quantum groups, including arbitrary compact Kac algebras. In the latter setting, we show, in addition, that $mathcal{Z}(L^1(mathbb{G}))$ is a completely complemented $mathcal{Z}(L^1(mathbb{G}))$-submodule of $L^1(mathbb{G})$.
We show that there is a one-to-one correspondence between compact quantum subgroups of a co-amenable locally compact quantum group $mathbb{G}$ and certain left invariant C*-subalgebras of $C_0(mathbb{G})$. We also prove that every compact quantum sub
This is a short survey on idempotent states on locally compact groups and locally compact quantum groups. The central topic is the relationship between idempotent states, subgroups and invariant C*-subalgebras. We concentrate on recent results on loc
Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital $*$-subalgebra with core-like properties in its domain. On the other hand we prove that every normalised, s
In this paper we study weight
Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold is stably parallelizable then it is shown that the compact quantum grou