OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
| dc.contributor.author | Marcoux, Laurent W. | |
| dc.contributor.author | Radjavi, Heydar | |
| dc.contributor.author | Zhang, Yuanhang | |
| dc.date.accessioned | 2022-05-10T19:48:33Z | |
| dc.date.available | 2022-05-10T19:48:33Z | |
| dc.date.issued | 2020-12-15 | |
| dc.description | The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2020.07.036. © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license | en |
| dc.description.abstract | Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥A|ran P is said to be an off-diagonal corner of A, and L is said to be essential if ∩{ker L : L ∈ L} = {0} and ∩{ker L ∗ : L ∈ L} = {0}, where L ∗ denotes the adjoint of L. Our goal in this paper is to determine effective upper bounds on dim A in terms of dim L, where L is an essential off-diagonal corner of A. A detailed structure analysis of A based upon the dimension of L, while seemingly elusive in general, is nevertheless provided in the cases where dim L ∈ {1, 2}. | en |
| dc.description.sponsorship | Research supported in part by NSERC (Canada). Research was supported in part by Science and Technology Development Project of Jilin Province (No.:20190103028JH), National Natural Science Foundation of China (No.:11601104, 11671167, 11201171) and China Scholarship Council (No.:201806175122). | en |
| dc.identifier.uri | https://doi.org/10.1016/j.laa.2020.07.036 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18254 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | off-diagonal corners | en |
| dc.subject | compressions of matrices | en |
| dc.title | OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn) | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Marcoux, L. W., Radjavi, H., & Zhang, Y. (2020). Off-diagonal corners of subalgebras of L(Cn). Linear Algebra and Its Applications, 607, 58–88. https://doi.org/10.1016/j.laa.2020.07.036 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |
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