Brief communications

On the distribution of eigenvalues of nuclear operators

O. I. Reinov

Saint Petersburg State University, Saint Petersburg, Russia

Abstract: It is shown how certain recent results in the theory of determinants and traces can be applied to obtain new theorems on the distribution of eigenvalues of nuclear operators on Banach spaces and to prove the equality of the spectral and nuclear traces of such operators. As an example, we consider a new class of operators: the class of generalized Lapresté nuclear operators.

Keywords: $\alpha$-nuclear operator, determinant, trace, eigenvalue.

Received: 17.02.2023
Accepted: 14.11.2023

DOI: 10.4213/faa4100

 English version: Functional Analysis and Its Applications, 2024, 58:3, 344–346

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