Compact operators in the C ∗ -algebra generated by a matrix weighted shift

Dianlu Tian; Lining Jiang

doi:10.1007/s43034-020-00074-w

Compact operators in the C ^∗ -algebra generated by a matrix weighted shift

Dianlu Tian^*, Lining Jiang

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

Abstract

Complex symmetry operators have notable applications in extension and dilation results, rank one perturbations of Jordan operators, matrix-valued inner functions and free interpolation theory in the disk and so on. While in the study of the complex symmetric operators, one of the problems one always encounters is when a C^∗-algebra singly generated contains no nonzero compact operators. In this paper, we answer this question recur to matrix weighted shift operators.

Original language	English
Pages (from-to)	1158-1169
Number of pages	12
Journal	Annals of Functional Analysis
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/s43034-020-00074-w
Publication status	Published - 1 Sept 2020

Keywords

C-algebra
Compact operator
Matrix weighted shift operator

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10.1007/s43034-020-00074-w

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abstract = "Complex symmetry operators have notable applications in extension and dilation results, rank one perturbations of Jordan operators, matrix-valued inner functions and free interpolation theory in the disk and so on. While in the study of the complex symmetric operators, one of the problems one always encounters is when a C∗-algebra singly generated contains no nonzero compact operators. In this paper, we answer this question recur to matrix weighted shift operators.",

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Compact operators in the C ^∗ -algebra generated by a matrix weighted shift

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Keywords

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