Commutator inequalities via Schur products

TY - GEN

T1 - Commutator inequalities via Schur products

AU - Christensen, Erik

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-319-39286-8

DO - 10.1007/978-3-319-39286-8

M3 - Article in proceedings

SN - 978-3-319-39284-4

T3 - Abel Symposia

SP - 127

EP - 143

BT - Operator Algebras and Applications

A2 - Carlsen, Toke M.

A2 - Larsen, Nadia S.

A2 - Neshveyev, Sergey

A2 - Skau, Christian

PB - Springer

T2 - Abel Symposium 2015

Y2 - 7 August 2016 through 11 August 2016

ER -