Quasidiagonality of direct sums of weighted shifts
Author:
Sivaram K. Narayan
Journal:
Trans. Amer. Math. Soc. 332 (1992), 757774
MSC:
Primary 47B37; Secondary 47A66
MathSciNet review:
1012511
Fulltext PDF Free Access
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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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 D. Hadwin, Strongly quasidiagonal algebras, J. Operator Theory 18 (1987), 318. MR 912809 (89d:46060)
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 P. R. Halmos, Quasitriangular operators, Acta Sci. Math. (Szeged) 29 (1968), 283293. MR 0234310 (38:2627)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199210125119
PII:
S 00029947(1992)10125119
Keywords:
Quasidiagonality,
weighted shifts,
marked graphs,
crossed products of algebras
Article copyright:
© Copyright 1992 American Mathematical Society
