Positive definiteness of functions with applications to operator norm inequalities

DOI10.1090/S0065-9266-2010-00616-1zbMath1227.47005MaRDI QIDQ3091750

Hideki Kosaki

Publication date: 14 September 2011

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

logarithmic meanarithmetic meangeometric meanoperatorBochner's theoremunitarily invariant normharmonic meanHeinz meansHeinz-type norm inequality

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operator inequalities (47A63) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (22)

A norm inequality for some special functions ⋮ Cauchy–Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications ⋮ Positive-definiteness and integral representations for special functions ⋮ Positive solutions of a class of operator equations ⋮ Contractive maps on operator ideals and norm inequalities. II ⋮ Unitarily invariant norm inequalities for some means ⋮ Positive definiteness and infinite divisibility of certain functions of hyperbolic cosine function ⋮ Strong monotonicity for various means ⋮ Cauchy-Schwarz inequalities for inner product type transformers in \({Q}^*\) norm ideals of compact operators ⋮ Families of completely positive maps associated with monotone metrics ⋮ The measure transition problem for meromorphic polar functions ⋮ Complex variable positive definite functions ⋮ Refinements and reverses of Young type inequalities ⋮ Inertia of some conditionally negative definite matrices ⋮ Conditionally negative definite functions ⋮ Contractive maps on operator ideals and norm inequalities. III. ⋮ Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators ⋮ A certain generalization of the Heinz inequality for positive operators ⋮ Positive definiteness of certain functions and comparison of power difference and Heinz means ⋮ Arithmetic-geometric mean and related submajorisation and norm inequalities for \(\tau\)-measurable operators. II ⋮ Norm inequalities for elementary operators and other inner product type integral transformers with the spectra contained in the unit disc ⋮ Extensions of the arithmetic–geometric means and Young's norm inequalities to accretive operators, with applications

Cites Work

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• Interpolating the arithmetic--geometric mean inequality and its operator version
• Mean matrices and infinite divisibility
• Positive definite solutions of some matrix equations
• Norm inequalities in operator ideals
• Riemannian metrics on positive definite matrices related to means
• On the definiteness of the solutions of certain matrix equations
• Some remarks on interpolation theorems and the boundness or the triangular projection in unitary matrix spaces
• Arithmetic-geometric mean and related inequalities for operators
• Comparison of various means for operators
• Unitarily invariant norms under which the map \(A\to| A|\) is Lipschitz continuous
• Means of Hilbert space operators
• Double operator integrals in a Hilbert space
• On the exponential metric increasing property.
• Cauchy--Schwarz norm inequalities for weak*-integrals of operator valued functions
• Notes on matrix arithmetic-geometric mean inequalities
• Positive definite matrices
• On infinite divisibility of positive definite functions arising from operator means
• The matrix arithmetic-geometric mean inequality revisited
• Beiträge zur Störungstheorie der Spektralzerlegung
• Inequalities for hadamard product and unitarily invariant norms of matrices
• GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS
• Lipschitz Continuity of Functions of Operators in the Schatten Classes
• More Matrix Forms of the Arithmetic-Geometric Mean Inequality
• Inequalities for Unitarily Invariant Norms
• Positive Definite Functions and Operator Inequalities
• Means for matrices and comparison of their norms
• Sharp Inequalities for Some Operator Means
• Generalized Lyapunov Equations and Positive Definite Functions
• Infinitely Divisible Matrices
• The main triangle projection in matrix spaces and its applications
• Matrix inequalities

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