2023/03/18 by Pintu Bhunia, Bhunia, Pintu
Computer Science · Mathematics · #15A60 #47A12 #47A30 #47A63 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2303.10392
openalex publication_date 2023/03/18 · openalex created_date 2023/03/22 · openalex updated_date 2026/07/28
Let A=\beginbmatrix Aij \endbmatrix be an n× n operator matrix, where each Aij is a bounded linear operator on a complex Hilbert space. Among other numerical radius bounds, we show that w(A)≤ w(A), where A=\beginbmatrix aij \endbmatrix is an n× n complex matrix, with aij= \begincases w(Aii) when i=j, ‖ | Aij|+ | Aji^*| ‖1/2 ‖ | Aji|+ | Aij^*| ‖1/2 when ij . \endcases This is a considerable improvement of the existing bound w(A)≤ w(A), where A=\beginbmatrix aij \endbmatrix is an n× n complex matrix, with aij= \begincases w(Aii) when i=j, ‖Aij‖ when i≠ j. \endcases Further, applying the bounds, we develop the numerical radius bounds for the product of two operators and the commutator of operators. Also, we develop an upper bound for the spectral radius of the sum of the product of n pairs of operators, which improve the existing bound.