Operator Lipschitz functions on Banach spaces

Jan Rozendaal ; Fedor Sukochev ; Anna Tomskova

Studia Mathematica, Tome 233 (2016), p. 57-92 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X, Y be Banach spaces and let (X,Y) be the space of bounded linear operators from X to Y. We develop the theory of double operator integrals on (X,Y) and apply this theory to obtain commutator estimates of the form $||f(B)S - Sf(A)||_{(X,Y)} ≤ const||BS - SA||_{(X,Y)}$ for a large class of functions f, where A ∈ (X), B ∈ (Y) are scalar type operators and S ∈ (X,Y). In particular, we establish this estimate for f(t): = |t| and for diagonalizable operators on $X = ℓ_{p}$ and $Y = ℓ_{q}$ for p < q. We also study the estimate above in the setting of Banach ideals in (X,Y). The commutator estimates we derive hold for diagonalizable matrices with a constant independent of the size of the matrix.

Détail

Publié le : 2016-01-01

Zbl 06575023

EUDML-ID : urn:eudml:doc:285670