# Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space

## TL;DR

This paper develops an equivariant gradient degree theory for unbounded self-adjoint operators with discrete spectra in Hilbert spaces, enabling new analysis tools for symmetric operator perturbations.

## Contribution

It introduces a novel equivariant gradient degree framework tailored for unbounded self-adjoint operators with discrete spectra in Hilbert spaces.

## Key findings

- Provides a new mathematical tool for analyzing symmetric operator perturbations
- Extends degree theory to unbounded operators with discrete spectra
- Discusses potential applications in operator perturbation analysis

## Abstract

We present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.