Remarks on the classification of a pair of commuting semilinear operators

TL;DR

This paper extends a classical result by Gelfand and Ponomarev, demonstrating that classifying pairs of commuting semilinear operators is as complex as classifying k-tuples of such operators, highlighting the problem's inherent difficulty.

Contribution

It generalizes the classification problem from linear to semilinear operators, establishing an analogous complexity result for the semilinear case.

Findings

Proves the classification problem for pairs of commuting semilinear operators is as complex as for k-tuples.

Extends classical linear operator classification results to the semilinear setting.

Abstract

Gelfand and Ponomarev [Functional Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators.