“…Note that if A is accretive-dissipative, then W (e -iπ 4 A) ⊆ S π 4 . Recently this class of matrices has been studied by researchers partly due to the fact that it contains the class of positive semidefinite matrices (see, e.g., [1,[11][12][13][14][15][16][17]).…”
Section: ])mentioning
confidence: 99%
“…Bourahli et al [1,Lemma 3.4] showed that if A = A 11 A 12 A 21 A 22 ∈ M 2n is a positive semidefinite contraction and s, t are positive real numbers such that 1 s…”
Section: ])mentioning
confidence: 99%
“…A 21 A 22 ∈ M 2n be a sector matrix with W (A) ⊆ S α for some α ∈ [0, π/2). Then, for all r, s, t > 0 with 1 s + 1 t = 1 and all unitarily invariant norms,…”
Section: Theorem 24 Let F ∈ C Be An Increasing Submultiplicative Funmentioning
confidence: 99%
“…, λ n (A) of A are all real, we arrange them in nonincreasing order λ 1 (A) ≥ • • • ≥ λ n (A). Singular values of A are the eigenvalues of |A| and are arranged in nonincreasing order s 1…”
In this article, we show unitarily invariant norm inequalities for sector $2\times 2$
2
×
2
block matrices which extend and refine some recent results of Bourahli, Hirzallah, and Kittaneh (Positivity, 2020, 10.1007/s11117-020-00770-w).
“…Note that if A is accretive-dissipative, then W (e -iπ 4 A) ⊆ S π 4 . Recently this class of matrices has been studied by researchers partly due to the fact that it contains the class of positive semidefinite matrices (see, e.g., [1,[11][12][13][14][15][16][17]).…”
Section: ])mentioning
confidence: 99%
“…Bourahli et al [1,Lemma 3.4] showed that if A = A 11 A 12 A 21 A 22 ∈ M 2n is a positive semidefinite contraction and s, t are positive real numbers such that 1 s…”
Section: ])mentioning
confidence: 99%
“…A 21 A 22 ∈ M 2n be a sector matrix with W (A) ⊆ S α for some α ∈ [0, π/2). Then, for all r, s, t > 0 with 1 s + 1 t = 1 and all unitarily invariant norms,…”
Section: Theorem 24 Let F ∈ C Be An Increasing Submultiplicative Funmentioning
confidence: 99%
“…, λ n (A) of A are all real, we arrange them in nonincreasing order λ 1 (A) ≥ • • • ≥ λ n (A). Singular values of A are the eigenvalues of |A| and are arranged in nonincreasing order s 1…”
In this article, we show unitarily invariant norm inequalities for sector $2\times 2$
2
×
2
block matrices which extend and refine some recent results of Bourahli, Hirzallah, and Kittaneh (Positivity, 2020, 10.1007/s11117-020-00770-w).
We prove a spectral radius inequality for operator matrices with commuting entries. Applications of this inequality to the polynomial eigenvalue problem are also given.
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