Remarks on the classification of a pair of commuting semilinear operators

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.

15 pages

References in corpus (5)

• Canonical matrices for linear matrix problems
• Classification problems for system of forms and linear mappings
• Complexity of matrix problems
• Canonical matrices of isometric operators on indefinite inner product spaces
• Simultaneous unitary equivalences

Cited by in corpus (6)

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• Regularizing algorithm for mixed matrix pencils
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• Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras
• Cycles of linear and semilinear mappings
• Tame systems of linear and semilinear mappings