Differential structure on the dual of a compact lie group

C*-algebras with norm controlled dual limits and nilpotent Lie groups

Motivated by the description of the C*-algebras of 5 dimensional nilpotent Lie groups as algebras of operator fields defined over their spectra, we introduce the family of C* -algebras with norm controlled dual limits and we show that the C* -algebras of the 5 dimensional nilpotents Lie groups belong to this class.

Hardy's theorem for compact Lie groups

We show that Hardy's uncertainty principle can be reformulated in such a way that it has an analogue even for compact Lie groups and symmetric spaces of compact type.

Fourier algebra of a compact Lie group

Let G be a compact connected Lie group. We prove that the Fourier algebra A(G) is weakly amenable if and only if G is abelian.

Dual properties and joint spectra for solvable Lie algebras of operators

Given $L$ a solvable Lie Algebra of operators acting on a Banach space $E$, we study the action of the opposite algebra of $L$, $L'$, on $E^*$. Moreover, we extend Słodkowski joint spectra, $σ_{δ,k}$, $σ_{π,k}$, and we study its usual spectral properties.

Gohberg lemma, compactness, and essential spectrum of operators on compact Lie groups

In this paper we prove a version of the Gohberg lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators on compact Lie groups. As a consequence, we prove several results on bounds for the essential spectrum and a criterion for an operator to be compact. The conditions are given in terms of the matrix-valued symbols of operators.

Besov 与 Triebel--Lizorkin 空间在具有多项式增长的滤过李群上的研究，I：包含关系、离散化与对偶性

Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups with Polynomial Growth, I: Inclusions, Discretization, Duality

本文在具有多项式增长的滤过李群上，发展加权次强制算子相关的 Besov 与 Triebel-Lizorkin 空间理论，研究其等价定义、包含关系、离散化与对偶性。