Annals of Functional Analysis

Lifting problems for normed spaces

Niels Grønbæk

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A classical theorem of G. Köthe states that the Banach spaces X with the property that all bounded linear maps XY into an arbitrary Banach space Y can be lifted with respect to bounded linear surjections onto Y are up to topological linear isomorphism precisely the spaces 1(A). We extend this result to the category of normed linear spaces and bounded linear maps. This answers a question raised by A. Ya. Helemskiĭ.

Article information

Ann. Funct. Anal., Volume 7, Number 1 (2016), 118-126.

Received: 20 March 2015
Accepted: 9 June 2015
First available in Project Euclid: 27 November 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46M10: Projective and injective objects [See also 46A22]

lifting problems projectives noncomplete normed spaces Hahn–Banach theorem


Grønbæk, Niels. Lifting problems for normed spaces. Ann. Funct. Anal. 7 (2016), no. 1, 118--126. doi:10.1215/20088752-3429463.

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