Functiones et Approximatio Commentarii Mathematici

On the splitting relation for Frèchet-Hilbert spaces

Dietmar Vogt

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Abstract

A shorter proof is given for a theorem of Domański and Mastyło characterizing the pairs $(E,F)$ of Frèchet-Hilbert spaces with the property that every exact sequence $0\to F\to G\to E\to 0$ of Frèchet-Hilbert spaces splits. The results on acyclicity of inductive spectra of metrizable locally convex spaces which we use are also presented with proofs.

Article information

Source
Funct. Approx. Comment. Math., Volume 44, Number 2 (2011), 215-225.

Dates
First available in Project Euclid: 22 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.facm/1308749125

Digital Object Identifier
doi:10.7169/facm/1308749125

Mathematical Reviews number (MathSciNet)
MR2841180

Zentralblatt MATH identifier
1230.46005

Subjects
Primary: 46A04: Locally convex Fréchet spaces and (DF)-spaces
Secondary: 46M18: Homological methods (exact sequences, right inverses, lifting, etc.) 46M40: Inductive and projective limits [See also 46A13]

Keywords
Frèchet-Hilbert space exact sequence splitting condition inductive spectrum acyclic

Citation

Vogt, Dietmar. On the splitting relation for Frèchet-Hilbert spaces. Funct. Approx. Comment. Math. 44 (2011), no. 2, 215--225. doi:10.7169/facm/1308749125. https://projecteuclid.org/euclid.facm/1308749125


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References

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