Functiones et Approximatio Commentarii Mathematici

On the splitting relation for Frèchet-Hilbert spaces

Dietmar Vogt

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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

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

First available in Project Euclid: 22 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Frèchet-Hilbert space exact sequence splitting condition inductive spectrum acyclic


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.

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