@inproceedings{c192af46797045b8a5f6f4fc162089bf,
title = "Commutator inequalities via Schur products",
abstract = "For a self-adjoint unbounded operator D on a Hilbert space H; a bounded operator y on H and some Borel functions g(t) we establish inequalities of the type∥[g(D), y] ∥ ≤ A0∥y∥+1∥[D, y] ∥+A2∥[D, [D, y]] ∥++An∥[D, [D,. [D, y].]] ∥ ∥. The proofs take place in a space of infinite matrices with operator entries, and in this setting it is possible to approximate the matrix associated to [g(D), y] by the Schur product of a matrix approximating [D, y] and a scalar matrix. A classical inequality on the norm of Schur products may then be applied to obtain the results.",
author = "Erik Christensen",
year = "2016",
doi = "10.1007/978-3-319-39286-8",
language = "English",
isbn = "978-3-319-39284-4",
series = "Abel Symposia",
publisher = "Springer",
pages = "127--143",
editor = "Carlsen, {Toke M. } and Larsen, {Nadia S. } and Neshveyev, {Sergey } and Skau, {Christian }",
booktitle = "Operator Algebras and Applications",
note = "Abel Symposium 2015 ; Conference date: 07-08-2016 Through 11-08-2016",
}