Functiones et Approximatio Commentarii Mathematici

On the equality between two diametral dimensions

Françoise Bastin and Loïc Demeulenaere

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Abstract

The paper gives sufficient conditions to have the equality between two diametral dimensions of metrizable locally convex spaces and examples of Köthe echelon spaces satisfying them. It also provides examples for which the equality does not hold.

Article information

Source
Funct. Approx. Comment. Math., Volume 56, Number 1 (2017), 95-107.

Dates
First available in Project Euclid: 27 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1485486020

Digital Object Identifier
doi:10.7169/facm/1594

Mathematical Reviews number (MathSciNet)
MR3629013

Zentralblatt MATH identifier
06864148

Subjects
Primary: 46A63: Topological invariants ((DN), ($\Omega$), etc.)
Secondary: 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]

Keywords
diametral dimension Schwartz spaces Köthe sequence spaces

Citation

Bastin, Françoise; Demeulenaere, Loïc. On the equality between two diametral dimensions. Funct. Approx. Comment. Math. 56 (2017), no. 1, 95--107. doi:10.7169/facm/1594. https://projecteuclid.org/euclid.facm/1485486020


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References

  • A. Aytuna, J. Krone, T. Terzioglu, Imbedding of power series spaces and spaces of analytic functions, Manuscripta math., 67, (1990), 125–142.
  • L. Demeulenaere, Dimension diamétrale, espaces de suites, propriétés $(DN)$ et $(\Omega)$, Master's Thesis, University of Liège, 2014.
  • A. Dynin and B.S. Mytiagin, Criterion for Nuclearity in Terms of Approximative Dimension, Bull. Acad. Polon. Sci., III, 8 (1960), 535–540.
  • H. Jarchow, Locally Convex Spaces, Mathematische Leitfëden, Stuttgart, 1981.
  • E. Karapinar, V. Zarariuta, On Orlicz-power series spaces, Medit. J. Math., 7(4), (2010), 553–563.
  • R.G. Meise and D. Vogt, Introduction to Functional Analysis, Clarendon Press, Oxford, 1997, translated from German by M.S. Ramanujan.
  • A. Pietsch, Nuclear Locally Convex Spaces, Springer-Verlag, Berlin, 1972, translated from German by W. H. Ruckle.
  • M.S. Ramanujan and T. Terzioglu, Diametral dimensions of Cartesian products, stability of smooth sequence spaces and applications., J. Reine Angew. Math. 280 (1976), 163–171.
  • T. Terzioglu, Die diametrale Dimension von lokalkonvexen Räumen, Collect. Math. 20, 1 (1969), 49–99.
  • T. Terzioglu, Smooth sequence spaces and associated nuclearity, Proc. Amer. Math. Soc. 37, 2 (1973), 497–504.
  • T. Terzioglu, Stability of smooth sequence spaces, J. Reine Angew. Math. 276 (1975), 184–189.
  • T. Terzioglu, Diametral Dimension and Köthe Spaces, Turkish J. Math. 32, 2 (2008), 213–218.
  • T. Terzioglu, Quasinormability and diametral dimension, Turkish J. Math. 37, 5 (2013), 847–851.
  • D. Vogt, Lectures on Fréchet spaces, Lecture Notes, Bergische Universität Wuppertal, 2000.
  • A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New-York, 1979.
  • V. Zahariuta, Linear topologic invariants and their applications to isomorphic classifcation of generalized power spaces, Turkish J. Math. 20, 2 (1996), 237–289.