Off-diagonal corners of subalgebras ofL(Cn)
| Autor: | Yuanhang Zhang, L. W. Marcoux, Heydar Radjavi |
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| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Structure analysis Unital 010102 general mathematics Diagonal Orthographic projection Dimension (graph theory) 010103 numerical & computational mathematics Space (mathematics) 01 natural sciences Combinatorics Product (mathematics) Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Algebra over a field Mathematics |
| Zdroj: | Linear Algebra and its Applications. 607:58-88 |
| ISSN: | 0024-3795 |
| Popis: | Let n ∈ N , and consider C n equipped with the standard inner product. Let A ⊆ L ( C n ) be a unital algebra and P ∈ L ( C n ) 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 } . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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