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Browsing by Subject "partial isometry"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On the decomposition of families of quasinormal operators
    (2013) Burdak, Zbigniew
    The canonical injective decomposition of a jointly quasinormal family of operators is given. Relations between the decomposition of a quasinormal operator T and the decomposition of a partial isometry in the polar decomposition of T are described. The decomposition of pairs of commuting quasinormal partial isometries and its applications to pairs of commuting quasinormal operators is shown. Examples are given.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On unitary equivalence of bilateral operator valued weighted shifts
    (Wydawnictwa AGH, 2019) Kośmider, Jakub
    We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We provide an example of unitary equivalence between shifts with weights defined on $\mathbb{C}^2$ which cannot be given by any unitary operator of diagonal form. The paper also contains some remarks regarding unitary operators that can give unitary equivalence of bilateral operator valued weighted shifts.