lipschitz algebra
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Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6543-6549
Author(s):  
Morteza Essmaili ◽  
Amir Sanatpour

In this paper, we study ?-contractibility of natural Banach function algebras on a compact Hausdorff space. As a consequence, we characterize ?-contractibility of the Lipschitz algebra Lip(X,d?), for a compact metric space (X,d). We also characterize ?-contractibility of certain subalgebras of Lipschitz functions including rational Lipschitz algebras, analytic Lipschitz algebras and differentiable Lipschitz algebras.


2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Davood Alimohammadi ◽  
Sirous Moradi

Let be a compact metric space. In 1987, Bade, Curtis, and Dales obtained a sufficient condition for density of a subspace of little Lipschitz algebra in this algebra and in particular showed that is dense in , whenever . Let be a compact subset of . We define new classes of Lipchitz algebras for and for , consisting of those continuous complex-valued functions on such that and , respectively. In this paper we obtain a sufficient condition for density of a linear subspace of extended little Lipschitz algebra in this algebra and in particular show that is dense in , whenever .


2002 ◽  
Vol 45 (3) ◽  
pp. 681-692 ◽  
Author(s):  
Thomas Vils Pedersen

AbstractFor a closed set $E$ contained in the closed unit interval, we show that the big Lipschitz algebra $\varLambda_{\gamma}(E)$ $(0\lt\gamma\lt1)$ is sequentially weak$^{\ast}$ generated by its idempotents if and only if it is weak$^{\ast}$ generated by its idempotents if and only if the little Lipschitz algebra $\lambda_{\gamma}(E)$ is generated by its idempotents, and we describe a class of perfect symmetric sets for which this holds. Moreover, we prove that $\varLambda_1(E)$ is sequentially weak$^{\ast}$ generated by its idempotents if and only if $E$ is of measure zero. Finally, we show that the quotient algebras$$ \mathcal{A}_{\beta}/\overline{J_{\beta}(E)}^{\text{weak}^{\ast}} $$of the Beurling algebras need not be weak$^{\ast}$ generated by their idempotents, when $E$ is of measure zero and $\beta\ge\tfrac{1}{2}$.AMS 2000 Mathematics subject classification: Primary 46J10; 46J30; 26A16; 42A16


Author(s):  
Derek W. Robinson

AbstractLet (A, R, σ) be an abelian C*-dynamical system. Denote the generator of σ by δ0 and define A∞ = ∩n>1D (δ0n). Further define the Lipschitz algebra .If δ is a *-derivation from A∞ into A½, then it follows that δ is closable, and its closure generates a strongly continuous one-parameter group of *-automorphisms of A. Related results for local dissipations are also discussed.


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