## Illinois Journal of Mathematics

### The isometric extension of the into mapping from a $\scr L\sp \infty(\Gamma)$-type space to some Banach space

Guang-Gui Ding

#### Abstract

We give some conditions under which an "into" isometric mapping from the unit sphere of an $\mathcal{L}^{\infty}(\Gamma)$-type space (in particular, the atomic $AM$-space) to the unit sphere of some Banach space can be (real) linearly extended.

#### Article information

Source
Illinois J. Math., Volume 51, Number 2 (2007), 445-453.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138423

Digital Object Identifier
doi:10.1215/ijm/1258138423

Mathematical Reviews number (MathSciNet)
MR2342668

Zentralblatt MATH identifier
1136.46007

Subjects
Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46B20: Geometry and structure of normed linear spaces

#### Citation

Ding, Guang-Gui. The isometric extension of the into mapping from a $\scr L\sp \infty(\Gamma)$-type space to some Banach space. Illinois J. Math. 51 (2007), no. 2, 445--453. doi:10.1215/ijm/1258138423. https://projecteuclid.org/euclid.ijm/1258138423