Quasidiagonality of direct sums of weighted shifts

Sivaram K. Narayan

doi:10.1090/S0002-9947-1992-1012511-9

Quasidiagonality of direct sums of weighted shifts

Sivaram K. Narayan

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 P_n of projections of finite rank such that P_n →I strongly and AP_n − P_nA →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 language	English
Pages (from-to)	757-774
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	332
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1992-1012511-9
State	Published - Aug 1992

Keywords

Crossed products of C-algebras
Marked graphs
Quasidiagonality
Weighted shifts

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10.1090/S0002-9947-1992-1012511-9

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AB - 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.

KW - Crossed products of C-algebras

KW - Marked graphs

KW - Quasidiagonality

KW - Weighted shifts

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

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ER -

Quasidiagonality of direct sums of weighted shifts

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