Operator Lipschitz functions on Banach spaces

• Autorzy: Jan Rozendaal , Fedor Sukochev , Anna Tomskova
• Języki publikacji: EN

Abstrakty

EN

Let X, Y be Banach spaces and let 𝓛(X,Y) be the space of bounded linear operators from X to Y. We develop the theory of double operator integrals on 𝓛(X,Y) and apply this theory to obtain commutator estimates of the form
$||f(B)S - Sf(A)||_{𝓛(X,Y)} ≤ const||BS - SA||_{𝓛(X,Y)}$
for a large class of functions f, where A ∈ 𝓛(X), B ∈ 𝓛(Y) are scalar type operators and S ∈ 𝓛(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 𝓛(X,Y). The commutator estimates we derive hold for diagonalizable matrices with a constant independent of the size of the matrix.

Kategorie tematyczne

• 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
• 47A55: Perturbation theory
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 1
• Strony: 57-92

Daty

wydano

2016

Twórcy

autor

Jan Rozendaal

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

autor

Fedor Sukochev

• School of Mathematics & Statistics, University of NSW, Kensington, NSW 2052, Australia

autor

Anna Tomskova

• School of Mathematics & Statistics, University of NSW, Kensington, NSW 2052, Australia

Identyfikatory

DOI

10.4064/sm8499-3-2016