Approximate identities in Banach function algebras

Volume 226 / 2015

H. G. Dales, A. Ülger Studia Mathematica 226 (2015), 155-187 MSC: Primary 46B15; Secondary 46B28, 46B42, 47L10. DOI: 10.4064/sm226-2-3


In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to a uniform algebra. We shall also obtain results about Banach sequence algebras and Banach function algebras that are ideals in their second duals.


  • H. G. DalesDepartment of Mathematics and Statistics
    University of Lancaster
    Lancaster LA1 4YF, United Kingdom
  • A. ÜlgerDepartment of Mathematics
    Koç University
    34450 Sariyer–Istanbul, Turkey

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