Lp-Nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups

Abstract

Given a compact Lie group $G$, in this paper we give symbolic criteria for operators to be nuclear and r-nuclear on Lp-spaces, with applications to distribution of eigenvalues and trace formulae. Since criteria in terms of kernels are often not effective in view of Carleman's example, in this paper we adopt the symbolic point of view. The criteria here are given in terms of the concept of matrix symbols defined on the non-commutative analogue of the phase space $G\times \hat{G}$, where $\hat{G}$ is the unitary dual of $G$.

This is the second half of our paper arXiv:1303.3914 so there is overlap in the preliminaries section

References in corpus (2)

• Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
• On multipliers on compact Lie groups

Cited by in corpus (11)

• Kernel and symbol criteria for Schatten classes and $r$-nuclearity on compact manifolds
• Global functional calculus for operators on compact Lie groups
• $L^p$-boundedness and $L^p$-nuclearity of multilinear pseudo-differential operators on ${\mathbb{Z}}^n$ and the torus ${\mathbb{T}}^n$
• Gohberg lemma, compactness, and essential spectrum of operators on compact Lie groups
• Pseudo-differential operators associated to general type I locally compact groups
• Difference equations and pseudo-differential operators on ${\mathbb{Z}}^n$
• Approximation property and nuclearity on mixed-norm $L^p$, modulation and Wiener amalgam spaces
• Fourier multipliers in Hilbert spaces
• On the nuclear trace of Fourier integral operators in $L^p$-spaces
• Schatten properties, nuclearity and minimality of shift invariant spaces
• Nuclearity for Fourier integral operators in $L^p$-spaces