A Small Note About Lower Bound of Eigenvalues

TL;DR

This paper introduces a framework leveraging the max-min principle to establish lower bounds for eigenvalues in a Hilbert space, relating them to eigenvalues in another Hilbert space, aiding in spectral analysis.

Contribution

It presents a novel method to derive lower bounds of eigenvalues in Hilbert spaces using the max-min principle, connecting eigenvalues across different spaces.

Findings

Provides a new framework for lower eigenvalue bounds

Utilizes the max-min principle effectively

Facilitates spectral analysis in Hilbert spaces

Abstract

This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.