A note on a generalized Jordan form of an infinite upper triangular matrix
Adel Nailevich Abyzov, Alexander Maklakov · Linear and Multilinear Algebra · 2024
In this paper, several equivalent conditions for the existence of a generalized Jordan form for matrices of locally nilpotent linear operators acting on an infinite countable dimensional vector space are presented, and an example is given showing that these conditions are not always fulfilled, which means the existence of infinite upper triangular matrices that are not similar to any generalized infinite Jordan matrix. Besides, it is shown that these conditions are not applicable in the case of an arbitrary dimensional of a vector space.