Banach Journal of Mathematical Analysis

Cover-strict topologies, ideals, and quotients for some spaces of vector-valued functions

Terje Hõim and D. A. Robbins

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Abstract

Let X be a completely regular Hausdorff space, let D be a cover of X, and let π:EX be a bundle of Banach spaces (algebras). Let Γ(π) be the space of sections of π, and let Γb(π,D) be the subspace of Γ(π) consisting of sections which are bounded on each DD. We study the subspace (ideal) and quotient structures of some spaces of vector-valued functions which arise from endowing Γb(π,D) with the cover-strict topology.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 4 (2016), 783-799.

Dates
Received: 10 August 2015
Accepted: 18 January 2016
First available in Project Euclid: 20 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1474373753

Digital Object Identifier
doi:10.1215/17358787-3649458

Mathematical Reviews number (MathSciNet)
MR3548626

Zentralblatt MATH identifier
1362.46045

Subjects
Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 46H10: Ideals and subalgebras

Keywords
cover-strict topology bundle of Banach spaces bundle of Banach algebras

Citation

Hõim, Terje; Robbins, D. A. Cover-strict topologies, ideals, and quotients for some spaces of vector-valued functions. Banach J. Math. Anal. 10 (2016), no. 4, 783--799. doi:10.1215/17358787-3649458. https://projecteuclid.org/euclid.bjma/1474373753


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References

  • [1] Mati Abel, J. Arhippainen, and J. Kauppi, Description of closed ideals in function algebras containing continuous unbounded functions, Mediterr. J. Math 7 (2010), no. 3, 271–282.
  • [2] M. Abel, J. Arhippainen, and J. Kauppi, Stone-Weierstrass type theorems for algebras containing continuous unbounded functions, Sci. Math. Jpn. 71 (2010), no. 1, 1–10.
  • [3] M. Abel, J. Arhippainen and J. Kauppi, Description of quotient algebras in function algebras containing continuous unbounded functions, Cent. Eur. J. Math. 10 (2012), no. 3, 1060–1066.
  • [4] H. Arizmendi-Peimbert, A. Carillo-Hoyo, and A. García, A spectral synthesis property for $C_{b}(X,\beta)$, Comment. Math. 48 (2008), no. 2, 121–127.
  • [5] G. Gierz, Bundles of Topological Vector Spaces and their Duality, with an appendix by the author and Klaus Keimel, Lecture Notes in Math. 955, Springer, Berlin, 1982.
  • [6] T. Hõim and D. A. Robbins, Strict topologies on spaces of vector-valued functions, Acta Comment. Univ. Tartu. Math. 14 (2010), 75–90.
  • [7] T. Hõim and D. A. Robbins, Spectral synthesis and other results in some topological algebras of vector-valued functions, Quaest. Math. 34 (2011), no. 1, 361–376.
  • [8] T. Hõim and D. A. Robbins, “Amenability as a hereditary property in some algebras of vector-valued functions” in Function Spaces in Analysis (Edwardsville, IL, 2014), Contemp. Math. 645, Amer. Math. Soc., Providence, 2015, 135–144.
  • [9] L. A. Khan, Linear Topological Spaces of Vector-valued Functions, available at https://www.researchgate.net/publication/254559506.
  • [10] J. W. Kitchen and D. A. Robbins, Gelfand representation of Banach modules, Dissertationes Math. (Rozprawy Mat.) 203 (1982), 47 pp.
  • [11] J. W. Kitchen and D. A. Robbins, Bundles of Banach algebras, Int. J. Math. Math. Sci. 17 (1994), no. 4, 671–680.
  • [12] J. W. Kitchen and D. A. Robbins, Maximal ideals in algebras of vector-valued functions, Int. J. Math. Math. Sci. 19 (1996), no. 3, 549–554.
  • [13] L. Nachbin, Elements of Approximation Theory, Van Nostrand, Princeton, 1967.
  • [14] C. Podara, Criteria of existence of bounded approximate identities in topological algebras, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 5, 949–960.
  • [15] J. Prolla, Approximation of Vector Valued Functions, North-Holland, Amsterdam, 1977.