On fully operator Lipschitz functions
نویسنده
چکیده
Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions on D; and (3) the class of operator Lipschitz functions on all contraction operators. A similar result is obtained for the class of operator C2-Lipschitz functions from A(D). © 2007 Elsevier Inc. All rights reserved.
منابع مشابه
Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...
متن کاملCompact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کاملWeighted composition operators between Lipschitz algebras of complex-valued bounded functions
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
متن کامل(DELTA,GAMMA, 2)-BESSEL LIPSCHITZ FUNCTIONS IN THE SPACE L_{2,ALPHA}(R+)
Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).
متن کاملTitchmarsh theorem for Jacobi Dini-Lipshitz functions
Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...
متن کامل