Differentiation of operator functions and perturbation bounds

DOI10.1007/s002200050279zbMath0918.47017OpenAlexW2023954531MaRDI QIDQ1270125

Dinesh Singh, Rajendra Bhatia, Kalayan B. Sinha

Publication date: 19 August 1999

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050279

zbMATH Keywords

perturbation boundsdifferentiation of operator functionsreduction of a noncommutative problem to a commutativeset of positive Hilbert space operators

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60)

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Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ Derivatives of symplectic eigenvalues and a Lidskii type theorem ⋮ Lipschitz type inequalities for noncommutative perspectives of operator monotone functions in Hilbert spaces ⋮ Some inequalities for analytic functions in Banach algebras ⋮ Second derivative Lipschitz type inequalities for an integral transform of positive operators in Hilbert spaces ⋮ Derivations, derivatives and chain rules ⋮ Perturbation bounds for matrix functions ⋮ Integral inequalities of the Hermite-Hadamard type for \(K\)-bounded norm-convex mappings ⋮ Vector norm inequalities for power series of operators in Hilbert spaces ⋮ Hermite-Hadamard type inequalities for functions whose derivatives are operator convex ⋮ Higher order derivatives and perturbation bounds for determinants ⋮ LIPSCHITZ-TYPE INEQUALITIES FOR ANALYTIC FUNCTIONS IN BANACH ALGEBRAS

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