Quasidiagonality of direct sums of weighted shifts

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Let ℋ be a separable Hubert space. A bounded linear operator A defined on ℋ is said to be quasidiagonal if there exists a sequence Pn of projections of finite rank such that Pn →I strongly and APn − PnA →0 as n → ∞. We give a necessary and sufficient condition for a finite direct sum of weighted shifts to be quasidiagonal. The condition is stated using a marked graph (a graph with a (0), (+) or (−) attached to its vertices) that can be associated with the direct sum.

Original languageEnglish
Pages (from-to)757-774
Number of pages18
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - Aug 1992


  • Crossed products of C-algebras
  • Marked graphs
  • Quasidiagonality
  • Weighted shifts


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