The Jordan form of a bitriangular operator
A Hilbert space operator T is called triangular if it has an upper triangular matrix with respect to some orthogonal basis of the underlying space. When both T and \(T^*\) are triangular, T is called bitriangular. The Jordan form J(T) of a bitriangular operator T is defined and the authors show that T is quasisimilar to J(T). This yields many consequences. They obtain a complete description of the quasisimilarity orbit \({\mathcal Q}{\mathcal S}(T)\) of a bitriangular operator T. They also study the spectra and the relationship between \({\mathcal Q}{\mathcal S}(T)\) and the closure of the similarity orbit. Moreover they use their results to study the structure of an important sublattice of hyperinvariant subspaces of a bitriangular operator. Many problems are stated throughout the paper.
scientific article; zbMATH DE number 4208870
scientific article