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Around the closure of the set of commutators of idempotents in B(H): Biquasitriangularity and factorisation

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1-s2.0-S0022123623000113-main.pdf (640.45 KB)

Date

2023-04-15

Authors

Marcoux, Laurent
Radjavi, Heydar
Zhang, Yuanhang

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

In this paper, we continue our study of the norm-closure of the set CEof bounded linear operators acting on a complex, infinite-dimensional, separable Hilbert space Hwhich may be expressed as the commutator of two idempotent operators. In particular, we identify which biquasitriangular operators belong to the norm-closure clos(CE)of CE, and we exhibit an index obstruction to membership in clos(CE). Finally, we consider factorisations of bounded linear operators on Has sums and products of elements in CEand related sets.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.jfa.2023.109854. © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

commutators, idempotents, biquasitriangular, index, factorisation

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Citation

URI

https://doi.org/10.1016/j.jfa.2023.109854
 http://hdl.handle.net/10012/20325

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Waterloo Research