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Davood Alimohammadi

Davood Alimohammadi

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-9398-6213
Education: PhD.
ScopusId: 6505995626
HIndex:
Faculty: Science
Address: Arak University
Phone:

Research

Title
Sufficient Conditions for Density in Extended Lipschitz Algebras
Type
JournalPaper
Keywords
Banach function algebra؛ Dense subspace؛ Extended Lipschitz algebra؛ Separation property
Year
2014
Journal Caspian Journal of Mathematical Sciences
DOI
Researchers Davood Alimohammadi ، Sirous Moradi

Abstract

Abstract. Let (X, d) be a compact metric space and let K be a nonempty compact subset of X. Let α ∈ (0, 1] and let Lip(X, K, dα ) denote the Banach algebra of all continuous complex-valued functions f on X for which pα,K(f) = sup{ |f(x)−f(y)| dα(x,y) : x, y ∈ K, x 6= y} < ∞ when equipped the algebra norm ||f||Lip(X,K,dα) = ||f||X + pα,K(f), where ||f||X = sup{|f(x)| : x ∈ X}. We denote by lip(X, K, dα ) the closed subalgebra of Lip(X, K, dα ) consisting of all f ∈ Lip(X, K, dα ) for which |f(x)−f(y)| dα(x,y) → 0 as d(x, y) → 0 with x, y ∈ K. In this paper we obtain a sufficient condition for density of a linear subspace or a subalgebra of Lip(X, K, dα ) in (Lip(X, K, dα ), || · ||Lip(X,K,dα)) (lip(X, K, dα ) in (lip(X, K, dα ), || · ||Lip(X,K,dα)), respectively). In particular, we show that the Lipschitz algebra Lip(X, dα ) is dense in (Lip(X, K, dα ), k · kLip(X,K,dα)) for α ∈ (0, 1] and Lip(X, d) and the little Lipschitz algebra lip(X, dα ) are dense in (lip(X, K, dα ), k · kLip(X,K,dα)) for α ∈ (0, 1).