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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
Some Dense Linear Subspaces of Extended Little Lipschitz Algebras
Type
JournalPaper
Keywords
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Year
2012
Journal ISRN Mathematical Analysis
DOI
Researchers Davood Alimohammadi ، Sirous Moradi

Abstract

Let ( 𝑋 , 𝑑 ) be a compact metric space. In 1987, Bade, Curtis, and Dales obtained a sufficient condition for density of a subspace 𝑃 of little Lipschitz algebra l i p ( 𝑋 , 𝛼 ) in this algebra and in particular showed that L i p ( 𝑋 , 1 ) is dense in l i p ( 𝑋 , 𝛼 ) , whenever 0 < 𝛼 < 1 . Let 𝐾 be a compact subset of 𝑋 . We define new classes of Lipchitz algebras L i p ( 𝑋 , 𝐾 , 𝛼 ) for 𝛼 ∈ ( 0 , 1 ] and l i p ( 𝑋 , 𝐾 , 𝛼 ) for 𝛼 ∈ ( 0 , 1 ) , consisting of those continuous complex-valued functions 𝑓 on 𝑋 such that 𝑓 | 𝐾 ∈ L i p ( 𝐾 , 𝛼 ) and 𝑓 | 𝐾 ∈ l i p ( 𝐾 , 𝛼 ) , respectively. In this paper we obtain a sufficient condition for density of a linear subspace 𝑃 of extended little Lipschitz algebra l i p ( 𝑋 , 𝐾 , 𝛼 ) in this algebra and in particular show that L i p ( 𝑋 , 𝐾 , 1 ) is dense in l i p ( 𝑋 , 𝐾 , 𝛼 ) , whenever 0 < 𝛼 < 1 .