Multiple operator integrals and higher operator derivatives
By V. Peller. 2005
118 citations recorded by the source corpus.
Abstract In this paper we consider the problem of the existence of higher derivatives of the function t ↦ ϕ ( A + tK ) , where ϕ is a function on the real line, A is a self-adjoint operator, and K is a bounded self-adjoint operator. We improve earlier results by Sten’kin. In order to do this, we give a new approach to multiple operator integrals. This approach improves the earlier approach given by Sten’kin. We also consider a similar problem for unitary operators.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6d82d664149348bc880e9d137cb1ca5123da3a5d
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In Applied Mathematics
- Fedor Sukochev
- D. Potapov
- V. Peller
- Alan L. Carey
- A. Skripka
- P. Dodds
- Nurulla Azamov
- Richard C. Bradley
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Operator Integrals, Spectral Shift, and Spectral Flow (2007, background): “Peller [32], where a similar approach to the theory of multiple operator integrals is presented in the setting of type I von Neumann algebras.”
- Spectral shift function of higher order (2009, background): “Recall that for f ∈ Wn, the operator derivative dn dtn [ f (H + tV)] is given by the integral Tf [n] [2, 20] where f [n] is the divided difference.”
- Multiple operator integrals in perturbation theory (2015, background): “In [57]multiple operator integralswere defined for functions that belong to the integral projective tensor product L∞(E1)⊗̂i · · · ⊗̂iL∞(Em).”
- Noncommutative Riesz transforms -- a probabilistic approach (2008, unknown): “[Pet] J. Peterson. l2-rigidity in von Neumann algebras. math.”