Functiones et Approximatio Commentarii Mathematici

An operator space characterization of Fréchet spaces not containing $l^1$

Wolfgang M. Ruess

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The classes of Fréchet spaces not containing $l^1$, of Gelfand-Phillips spaces, and of dual Gelfand-Phillips spaces are characterized by (pre)compactness criteria for sets of bounded linear operators transforming bounded sets into precompact sets.

Article information

Funct. Approx. Comment. Math., Volume 44, Number 2 (2011), 259-264.

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 46B03: Isomorphic theory (including renorming) of Banach spaces
Secondary: 46A032

Locally convex spaces no-containment of $l^1$ limited sets precompact operators


Ruess, Wolfgang M. An operator space characterization of Fréchet spaces not containing $l^1$. Funct. Approx. Comment. Math. 44 (2011), no. 2, 259--264. doi:10.7169/facm/1308749128.

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