Rocky Mountain Journal of Mathematics

On algebras of Banach algebra-valued bounded continuous functions

Hugo Arizmendi-Peimbert, Angel Carrillo-Hoyo, and Alejandra García-García

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let $X$ be a completely regular Hausdorff space. We denote by $C(X,A)$ the algebra of all continuous functions on $X$ with values in a complex commutative unital Banach algebra $A$. Let $C_{b}(X,A)$ be its subalgebra consisting of all bounded continuous functions and endowed with the uniform norm. In this paper, we give conditions equivalent to the density of a natural continuous image of $X\times \mathcal {M}(A)$ in the maximal ideal space of $C_{b}(X,A)$.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 2 (2016), 389-398.

Dates
First available in Project Euclid: 26 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1469537468

Digital Object Identifier
doi:10.1216/RMJ-2016-46-2-389

Mathematical Reviews number (MathSciNet)
MR3529074

Zentralblatt MATH identifier
1356.46033

Subjects
Primary: 46E40: Spaces of vector- and operator-valued functions 46H05: General theory of topological algebras 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]

Keywords
Banach algebras vector-valued bounded continuous functions maximal ideal space

Citation

Arizmendi-Peimbert, Hugo; Carrillo-Hoyo, Angel; García-García, Alejandra. On algebras of Banach algebra-valued bounded continuous functions. Rocky Mountain J. Math. 46 (2016), no. 2, 389--398. doi:10.1216/RMJ-2016-46-2-389. https://projecteuclid.org/euclid.rmjm/1469537468


Export citation

References

  • J. Arhippainen, On the ideal structure of algebras of LMC-algebras valued functions, Stud. Math. 101 (1992), 311–318.
  • R.C. Buck, Continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104.
  • S. Dierolf, K.H. Schröder and J. Wengenroth, Characters on certain function algebras, Funct. Approx. Comm. Math. 26 (1998), 53–58.
  • W.E. Dietrich, Jr., The maximal ideal space of the topological algebra $C(X,E)$, Math. Ann. 183 (1969), 201–212.
  • Z. Ercan and S. Onal, A remark on the homomorphism on $C(X)$, Proc. Amer. Math. Soc. 133 (12) (2005), 3609–3611.
  • W. Govaerts, Homomorphisms of weighted algebras of continuous functions, Ann. Mat. Pura Appl. 116 (1978), 151–158.
  • A. Hausner, Ideals in a certain Banach algebra, Proc. Amer. Math. Soc. 8 (1957), 246–259.
  • W.J. Hery, Maximal ideal in algebras of topological algebra valued functions, Pac. J. Math. 65 (1976), 365–373.
  • L.A Kahn, Linear topological spaces of continuous vector-valued functions, Academic Publ., Ltd., 2013-DOI: 10.12732/acadpubl.201301.
  • M.A. Naimark, Normed algebras, 1972, Wolters-Noordhoff Publishing, Groningen, The Netherlands, 1972.
  • C.E. Rickart, General theory of Banach algebras, R.E. Krieger Publishing Company, Huntington, NY, 1974 (original edition, D. Van Nostrand Reinhold, 1960).