| Autor: |
Chan, J. T., Li, C. K., Poon, Y. T. |
| Předmět: |
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| Zdroj: |
Linear & Multilinear Algebra; Jul2022, Vol. 70 Issue 11, p2178-2186, 9p |
| Abstrakt: |
Let H be an infinite dimensional complex Hilbert space and let B (H) be the algebra of all bounded linear operators on H . For every positive integer k and A ∈ B (H) , the k-numerical range of A is the set W k (A) = ∑ j = 1 k ⟨ A x j , x j ⟩ : { x 1 , ... , x k } is an orthonormal set in H . In this note, we show that the closure of W k (A) can be written as the convex hull of sets involving the essential numerical range of A and W ℓ (A) for 1 ≤ ℓ ≤ k. We also show that if W k (A) is closed, then W ℓ (A) is also closed for 1 ≤ ℓ ≤ k. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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