Lifting Problems for Normed Spaces

TY - JOUR

T1 - Lifting Problems for Normed Spaces

AU - Grønbæk, Niels

PY - 2016

Y1 - 2016

N2 - A classical theorem of G. Köthe states that the Banach spaces X with the property that all bounded linear maps X → Y 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 ℓ1(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.

AB - A classical theorem of G. Köthe states that the Banach spaces X with the property that all bounded linear maps X → Y 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 ℓ1(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.

U2 - 10.1215/20088752-3429463

DO - 10.1215/20088752-3429463

M3 - Journal article

SN - 2008-8752

VL - 7

SP - 118-126.

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

IS - 1

ER -