Weingarten integration over noncommutative homogeneous spaces

Metric Aspects of Noncommutative Homogeneous Spaces

For a closed cocompact subgroup Γ of a locally compact group G, given a compact abelian subgroup K of G and a homomorphism ρ : K̂ → G satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations C∗(Ĝ/Γ, ρ) of the homogeneous space G/Γ, generalizing Rieffel’s construction of quantum Heisenberg manifolds. We show that when G is a Lie group and G/Γ is conn...

Noncommutative Orlicz spaces over W *-algebras

Using the Falcone–Takesaki theory of noncommutative integration, we construct a family of noncommutative Orlicz spaces that are canonically associated to an arbitrary W *-algebra without any choice of weight involved, and we show that this construction is functorial over the category of W *-algebras with *-isomorphisms as arrows. MSC2010: 46L52, 46L51, 46M15.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Homogeneous holomorphic hermitian principal bundles over hermitian symmetric spaces

We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible generalizations, the general setup of invariant holomorphic principal fibre bundles is described in a systematic way.