Functiones et Approximatio Commentarii Mathematici

Bornological projective limits of inductive limits of normed spaces

Josè Bonet and Sven-Ake Wegner

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Abstract

We establish a criterion to decide when a countable projective limit of countable inductive limits of normed spaces is bornological. We compare the conditions occurring within our criterion with well-known abstract conditions from the context of homological algebra and with conditions arising within the investigation of weighted PLB-spaces of continuous functions.

Article information

Source
Funct. Approx. Comment. Math., Volume 44, Number 2 (2011), 227-242.

Dates
First available in Project Euclid: 22 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.facm/1308749126

Digital Object Identifier
doi:10.7169/facm/1308749126

Mathematical Reviews number (MathSciNet)
MR2841181

Zentralblatt MATH identifier
1242.46004

Subjects
Primary: 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
Secondary: 46A03: General theory of locally convex spaces 46A04: Locally convex Fréchet spaces and (DF)-spaces 46A08: Barrelled spaces, bornological spaces 46E10: Topological linear spaces of continuous, differentiable or analytic functions 46M40: Inductive and projective limits [See also 46A13]

Keywords
Locally convex spaces bornological spaces projective limits inductive limits weighted spaces of continuous functions

Citation

Bonet, Josè; Wegner, Sven-Ake. Bornological projective limits of inductive limits of normed spaces. Funct. Approx. Comment. Math. 44 (2011), no. 2, 227--242. doi:10.7169/facm/1308749126. https://projecteuclid.org/euclid.facm/1308749126


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