Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 1 (2016), 118-126.
Lifting problems for normed spaces
A classical theorem of G. Köthe states that the Banach spaces with the property that all bounded linear maps into an arbitrary Banach space can be lifted with respect to bounded linear surjections onto are up to topological linear isomorphism precisely the spaces . We extend this result to the category of normed linear spaces and bounded linear maps. This answers a question raised by A. Ya. Helemskiĭ.
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
Permanent link to this document
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]
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