Operator Integrals, Spectral Shift, and Spectral Flow
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Publication:3624529
DOI10.4153/CJM-2009-012-0zbMath1163.47008arXivmath/0703442MaRDI QIDQ3624529
Pheodor A. Sukochev, Nurulla A. Azamov, Peter G. Dodds, Alan L. Carey
Publication date: 30 April 2009
Published in: Canadian Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0703442
Perturbation theory of linear operators (47A55) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Noncommutative measure and integration (46L51) Transformers, preservers (linear operators on spaces of linear operators) (47B49)
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Trace formulas for additive and non-additive perturbations ⋮ Multiple operator integrals in perturbation theory ⋮ Perturbation theory and higher order \(\mathcal{S}^{p}\)-differentiability of operator functions ⋮ The Spectral Shift Function and the Witten Index ⋮ Higher order spectral shift ⋮ Spectral shift functions and Dirichlet-to-Neumann maps ⋮ Estimates and trace formulas for unitary and resolvent comparable perturbations ⋮ Asymptotically efficient estimation of smooth functionals of covariance operators ⋮ Itô's formula for noncommutative \(C^2\) functions of free Itô processes ⋮ Spectral shift function of higher order ⋮ Multilinear Schur multipliers and Schatten properties of operator Taylor remainders ⋮ Trace formulae for perturbations of class \(s_m\) ⋮ Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups ⋮ Numerical Solution of Free Stochastic Differential Equations ⋮ Non-commutative geometry and cyclic homology. Abstracts from the workshop held July 31 -- August 6, 2022 ⋮ Diagonality modulo hybrid Lorentz-\((p,1)\) ideals in semifinite factors ⋮ A general Dixmier trace formula for the density of states on open manifolds ⋮ Noncommutative \(C^k\) functions and Fréchet derivatives of operator functions ⋮ The Birman-Schwinger principle on the essential spectrum ⋮ Perturbation formulas for traces on normed ideals ⋮ A noncommutative generalisation of a problem of Steinhaus ⋮ Fréchet differentiability of the norm of $L_p$-spaces associated with arbitrary von Neumann algebras ⋮ Fréchet differentiability of the norm of \(L_p\)-spaces associated with arbitrary von Neumann algebras ⋮ On the Arazy conjecture concerning Schur multipliers on Schatten ideals ⋮ HIGHER ORDER DIFFERENTIABILITY OF OPERATOR FUNCTIONS IN SCHATTEN NORMS ⋮ Functions of perturbed dissipative operators ⋮ Higher order \(\mathcal{S}^2\)-differentiability and application to Koplienko trace formula ⋮ Trace formulas for resolvent comparable operators ⋮ The spectral shift function and spectral flow ⋮ Trace formulas for relative Schatten class perturbations ⋮ Isometric embeddability of \(S_q^m\) into \(S_p^n\) ⋮ Embeddings of operator ideals into \(\mathcal{L}_p\)-spaces on finite von Neumann algebras ⋮ Fréchet differentiability of \(\mathcal{S}^p\) norms ⋮ Asymptotic expansions for trace functionals ⋮ Third order trace formula ⋮ The index formula and the spectral shift function for relatively trace class perturbations ⋮ Functions of operators under perturbations of class \(S_p\) ⋮ Operator Hölder-Zygmund functions ⋮ Spectral averaging for trace compatible operators ⋮ Functions of unitary operators: derivatives and trace formulas ⋮ Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators ⋮ Operator Lipschitz functions on Banach spaces ⋮ Weak \((1,1)\) estimates for multiple operator integrals and generalized absolute value functions ⋮ Resolution of Peller's problem concerning Koplienko–Neidhardt trace formulae ⋮ Arithmetic-geometric mean and related submajorisation and norm inequalities for \(\tau\)-measurable operators. II ⋮ Necessary and sufficient conditions for 𝑛-times Fréchet differentiability on 𝒮^{𝓅}, 1<𝓅<∞ ⋮ Higher derivatives of operator functions in ideals of von Neumann algebras ⋮ Cyclic cocycles in the spectral action ⋮ Derivations with values in the ideal of \(\tau\)-compact operators affiliated with a semifinite von Neumann algebra ⋮ When do triple operator integrals take value in the trace class? ⋮ Singular traces and perturbation formulae of higher order
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