2023/08/18 by Pintu Bhunia, Bhunia, Pintu, Suvendu Jana +3
Computer Science · Mathematics · #15A60 #47A12 #47A30 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2308.09258
openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop several Euclidean operator radius bounds for the product of two d-tuple operators using positivity criteria of a 2× 2 block matrix whose entries are d-tuple operators. From these bounds, by using the polar decomposition of operators, we obtain Euclidean operator radius bounds for d-tuple operators. Among many other interesting bounds, it is shown that we(A) amp;\leqamp;\frac1√2 A‖1/2√‖∑k=1d (|Ak|+|Ak^*|)‖, where we(A) and ‖A‖ are the Euclidean operator radius and the Euclidean operator norm, respectively, of a d-tuple operator A=(A1,A2, …,Ad). Further, we develop an upper bound for the Euclidean operator radius of n× n operator matrix whose entries are d-tuple operators. In particular, it is proved that if \beginbmatrix \mathbfAij \endbmatrixn× n is an n× n operator matrix then we( \beginbmatrix \mathbfAij \endbmatrixn× n)≤ w (\beginbmatrix aij \endbmatrixn× n), where each \mathbfAij is a d-tuple operator, 1≤ i,j≤ n, aij=we(\mathbfAij) if i=j, aij= √we(|\mathbfAji|+|\mathbfAij^*|)we(|\mathbfAij|+|\mathbfAji^*|) if ij. Other related applications are also discussed.