A generalization of the Böttcher-Wenzel inequality for three rectangular matrices
Copyright policy )A generalization of the Böttcher-Wenzel inequality for three rectangular matrices
Let $m,n$ be positive integers. For all $m\times n$ complex matrices $A, C$ and an $n\times m$ matrix $B$, we define a generalized commutator as $ABC-CBA$. We estimate the Frobenius norm of it, and finally get the inequality, which is a generalization of the Böttcher-Wenzel inequality. If $n=1$ or $m=1$, then the Frobenius norm of $ABC-CBA$ can be estimated with a tighter upper bound.
9 pages
Operator Algebras, Rings and Algebras, Rings and Algebras (math.RA), FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis, 15A45, 15A60, 15A18, Functional Analysis (math.FA)
Operator Algebras, Rings and Algebras, Rings and Algebras (math.RA), FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis, 15A45, 15A60, 15A18, Functional Analysis (math.FA)
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