On products of $l_{s,r}$-nuclear and close operators

TL;DR

This paper investigates how products of different nuclear operators can be factored through Schatten-von Neumann operators in Hilbert spaces, with applications to eigenvalue problems.

Contribution

It introduces new factorization techniques for nuclear operators of various types via Schatten-von Neumann operators, expanding understanding of their structure and applications.

Findings

Established conditions for factorization of nuclear operator products.

Applied factorization results to eigenvalue estimation problems.

Extended existing theory of nuclear operators in Hilbert spaces.

Abstract

We study the possibilities of factorizations of products of nuclear operators of different types through the Schatten-von Neumann operators in Hilbert spaces with giving some applications to eigenvalues problems.