Some spectral results for certain positive operators in Hilbert Spaces

TL;DR

This paper explores the spectral properties of positive operators derived from matrices in linear complementarity problems, providing new factorizations and insights into their eigenvalues and spectral behavior.

Contribution

It introduces a spectral-based factorization of P-matrices into the product of two non-trivial P-matrices and analyzes their spectral properties.

Findings

Factorization of P-matrix into two non-trivial P-matrices.

Analysis of eigenvalues and spectral values of positive operators.

Enhanced understanding of spectral behavior in operator theory.

Abstract

This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics and its applications, including operator theory, functional analysis, and quantum mechanics. Understanding their spectral behavior is essential for analyzing the dynamics and stability of systems governed by such operators. P-matrix is one of the important types of matrices appearing in linear complementarity problems. In this research, with the help of spectral results we have given a factorization for P-matrix, as the product of two non-trivial P-matrices. We also focus on elucidating spectral properties such as eigenvalues, approximate eigenvalues and spectral values associated with certain positive operators.