# (h; k)-Dichotomy and Lyapunov Type Norms

## TL;DR

This paper introduces a generalized concept of nonuniform (h; k)-dichotomy for evolution operators in Banach spaces, providing characterizations via compatible norm families.

## Contribution

It extends the theory of dichotomies by defining (h; k)-dichotomy and offers new characterizations using norm families compatible with dichotomy projectors.

## Key findings

- Characterization of (h; k)-dichotomy in Banach spaces
- Introduction of norm families compatible with dichotomy projectors
- Extension of dichotomy theory to nonuniform cases

## Abstract

The paper considers a general concept of nonuniform (h; k)- dichotomy for evolution operators in Banach spaces. Two characterizations of this concept in terms of some families of norms compatible with the dichotomy projectors are given.