Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections
Let H be a complex separable Hilbert space and BH be the algebra of all bounded linear operators from H to H. Our goal in this article is to describe the closure of numerical range of parallel sum operator P:PQ for two orthogonal projections P and Q in BH as a closed convex hull of some explicit ell...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1448498 |
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| _version_ | 1832558467329556480 |
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| author | Weiyan Yu Ran Wang Chen Zhang |
| author_facet | Weiyan Yu Ran Wang Chen Zhang |
| author_sort | Weiyan Yu |
| collection | DOAJ |
| description | Let H be a complex separable Hilbert space and BH be the algebra of all bounded linear operators from H to H. Our goal in this article is to describe the closure of numerical range of parallel sum operator P:PQ for two orthogonal projections P and Q in BH as a closed convex hull of some explicit ellipses parameterized by points in the spectrum. |
| format | Article |
| id | doaj-art-92024ed6652b49489013f7843d4ba316 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-92024ed6652b49489013f7843d4ba3162025-02-03T01:32:21ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/1448498Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal ProjectionsWeiyan Yu0Ran Wang1Chen Zhang2College of Mathematics and StatisticsCollege of Mathematics and StatisticsCollege of Mathematics and StatisticsLet H be a complex separable Hilbert space and BH be the algebra of all bounded linear operators from H to H. Our goal in this article is to describe the closure of numerical range of parallel sum operator P:PQ for two orthogonal projections P and Q in BH as a closed convex hull of some explicit ellipses parameterized by points in the spectrum.http://dx.doi.org/10.1155/2024/1448498 |
| spellingShingle | Weiyan Yu Ran Wang Chen Zhang Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections Journal of Mathematics |
| title | Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections |
| title_full | Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections |
| title_fullStr | Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections |
| title_full_unstemmed | Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections |
| title_short | Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections |
| title_sort | geometric characterization of the numerical range of parallel sum of two orthogonal projections |
| url | http://dx.doi.org/10.1155/2024/1448498 |
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