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Operator Lipschitz functions on Banach spaces

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Rozendaal J., Sukochev F., Tomskova A.

Studia Mathematica

2016

tom 232

nr 1

57-92

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.

Ograniczanie wyników

1 Studia Mathematica

1 Rozendaal J.

1 Sukochev F.

1 Tomskova A.

1 2016

Wyniki wyszukiwania

Operator Lipschitz functions on Banach spaces