The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups Bu(Q) for Q ∈ GL(n,C) satisfying QQ̄ = ±In, n ≥ 2; (b) The quantum automorphism groups Aaut(B, τ) of finite dimensional C ∗-algebras B endowed with the canonical trace τ w...

Ramı́rez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight , Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of ...

Abstract We establish new results on the ‐approximation property for Banach operator ideal of unconditionally p ‐compact operators in case . As a consequence our results, we provide negative answer problem posed by Kim. Namely, implies neither nor (classical) approximation property; and property. Here, denotes Sinha Karn also show all that there is closed subspace fails

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

Abstract In [16], Peterzil and Steinhorn proved that if a group G definable in an o -minimal structure is not definably compact, then contains torsion-free subgroup of dimension 1. We prove here p -adic analogue the Peterzil–Steinhorn theorem, special case abelian groups. Let be -adically closed field M . If compact there H 1 which compact. future paper we will generalize this to non-abelian