Annals of Functional Analysis

Lifting problems for normed spaces

Niels Grønbæk

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1448591839

Digital Object Identifier
doi:10.1215/20088752-3429463

Mathematical Reviews number (MathSciNet)
MR3449344

Zentralblatt MATH identifier
1344.46051

Subjects
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]

Keywords
lifting problems projectives noncomplete normed spaces Hahn–Banach theorem

Citation

Grønbæk, Niels. Lifting problems for normed spaces. Ann. Funct. Anal. 7 (2016), no. 1, 118--126. doi:10.1215/20088752-3429463. https://projecteuclid.org/euclid.afa/1448591839


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References

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