Quasidiagonality of direct sums of weighted shifts

Author:
Sivaram K. Narayan

Journal:
Trans. Amer. Math. Soc. **332** (1992), 757-774

MSC:
Primary 47B37; Secondary 47A66

DOI:
https://doi.org/10.1090/S0002-9947-1992-1012511-9

MathSciNet review:
1012511

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a separable Hilbert space. A bounded linear operator defined on is said to be *quasidiagonal* if there exists a sequence of projections of finite rank such that strongly and as .

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 , or attached to its vertices) that can be associated with the direct sum.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1012511-9

Keywords:
Quasidiagonality,
weighted shifts,
marked graphs,
crossed products of -algebras

Article copyright:
© Copyright 1992
American Mathematical Society