# The generalized Ces\`{a}ro matrices of order three are supraposinormal on $\ell^2$

## TL;DR

This paper extends the analysis of generalized Cesàro matrices to order three, demonstrating they are supraposinormal on , and explores their related operator properties, suggesting further research on higher orders.

## Contribution

The paper adapts previous methods to prove that generalized Cesàro matrices of order three are supraposinormal on , providing new insights into their operator properties.

## Key findings

- Order three matrices are supraposinormal on 
- Results imply posinormality, coposinormality, hyponormality
- Conjecture proposed for higher orders

## Abstract

The procedure that was used in an earlier paper on the generalized Ces\`{a}ro matrices of order two is adapted here to show that generalized Ces\`{a}ro matrices of order three are supraposinormal on $\ell^2$. This leads to information about their posinormality, coposinormality, and hyponormality. The reader is then invited to formulate a conjecture regarding generalized Ces\`{a}ro matrices of other orders.