Noncommutative \(C^k\) functions and Fréchet derivatives of operator functions

DOI10.1016/j.exmath.2022.12.004OpenAlexW4287605641MaRDI QIDQ2694998

Evangelos A. Nikitopoulos

Publication date: 30 March 2023

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.03126

zbMATH Keywords

Fréchet derivative\(C^\ast\)-algebrafunctional calculusmultiple operator integral

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Functional calculus for linear operators (47A60) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Calculus of functions on infinite-dimensional spaces (26E15)

Related Items (1)

Itô's formula for noncommutative \(C^2\) functions of free Itô processes

Cites Work

• Multiple operator integrals in perturbation theory
• Theory of Besov spaces
• Hankel operators in the perturbation theory of unitary and self-adjoint operators
• Convex analysis and measurable multifunctions
• Higher order \(\mathcal{S}^2\)-differentiability and application to Koplienko trace formula
• Differentiation of operator functions in non-commutative \(L_{p}\)-spaces
• Higher derivatives of operator functions in ideals of von Neumann algebras
• When do triple operator integrals take value in the trace class?
• Itô's formula for noncommutative \(C^2\) functions of free Itô processes
• Multilinear Schur multipliers and Schatten properties of operator Taylor remainders
• Multiple operator integrals and higher operator derivatives
• Operator Lipschitz functions
• Hölder and locally Hölder Continuous Functions, and Open Sets of Class C^k, C^{k,lambda}
• Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization
• Operator Integrals, Spectral Shift, and Spectral Flow
• A First Course in Sobolev Spaces
• Necessary and sufficient conditions for 𝑛-times Fréchet differentiability on 𝒮^{𝓅}, 1<𝓅<∞
• HIGHER ORDER DIFFERENTIABILITY OF OPERATOR FUNCTIONS IN SCHATTEN NORMS
• Multilinear Operator Integrals
• Smooth analysis in Banach spaces
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