Kernel and symbol criteria for Schatten classes and $r$-nuclearity on compact manifolds

Abstract

In this note we present criteria on both symbols and integral kernels ensuring that the corresponding operators on compact manifolds belong to Schatten classes. A specific test for nuclearity is established as well as the corresponding trace formulae. In the special case of compact Lie groups, kernel criteria in terms of (locally and globally) hypoelliptic operators are also given. A notion of an invariant operator and its full symbol associated to an elliptic operator are introduced. Some applications to the study of $r$-nuclearity on $L^p$ spaces are also obtained.

8 pages. arXiv admin note: substantial text overlap with arXiv:1404.6479

References in corpus (1)

• Schatten classes on compact manifolds: Kernel conditions

Cited by in corpus (4)

• On some spectral properties of pseudo-differential operators on T
• Spectral properties of pseudo-differential operators over the compact group of $p$-adic integers and compact Vilenkin groups
• Nuclear pseudo-differential operators in Besov spaces on compact Lie groups
• Geometric maximizers of Schatten norms of some convolution type integral operators