Sentence examples for reductive spaces from inspiring English sources

The naturally reductive spaces have been investigated by a number of authors as a natural generalization of Riemannian symmetric spaces.

Most of the known examples of Banach homogeneous reductive spaces (see [AS2], [ARS], [CPR2], [MR] and [M]) are particular cases of this construction, which moreover generalizes them, for example, to representations of amenable, type I or almost connected groups.

Granted, the naked art spectator is a less common sight, but as our tour guide for the evening, Stuart Ringholt, tells it (he too in the nude), the white cube of an art museum is already a "reductive space"– so it follows that clothes are a kind of visual noise disrupting our experience.

We prove that R A, N) is an homogeneous reductive space under the action of the group GN, of invertible elements of N, and also an analytic submanifold of L A, N).

Here we give a simple proof of the fact that Gr0res(p) is a smooth submanifold of the affine Hilbert space p+B2(H), where B2(H) denotes the space of Hilbert Schmidt operators of H. Also we show that Gr0res(p) is a homogeneous reductive space.

Finally, we give a geometric criterion of homogeneous naturally reductive Randers spaces.

We now present a geometric criterion of homogeneous naturally reductive Randers spaces as Remark 3.1.

Sharp majorations for the meromorphic continuation of Eisenstein integrals for reductive symmetric spaces are proved.

The condition for the existence of discrete series representations forG/Hwas not known in general except for reductive symmetric spaces.

We generalize Casselman's pairing to p-adic reductive symmetric spaces and study the asymptotic behaviour of certain generalized coefficients.

We generalize this fact to the reductive symmetric spaces' case, the role of the exponential functions being taken by the Eisenstein integrals.