In this paper, we study irreducible unitary representations of GLn(R) and prove a number of results. Our first result establishes a precise connection between the annihilator of a representation and the existence of degenerate Whittaker functionals, thereby generalizing results of Kostant, Matumoto and others. Our second result relates the annihilator to the sequence of adduced representations,...

Let Λ be a lattice in an n-dimensional Euclidean space E and let Λ be a Minkowskian sublattice of Λ, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of Λ. We extend the classification of possible Z/dZ-codes of the quotients Λ/Λ to dimension 9, where dZ is the annihilator of Λ/Λ.

We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-TransueOrlicz space Mq (Ω, μ) with q > 2.