Annals of Functional Analysis

Isometries on the unit sphere of the $\ell^{1}$-sum of strictly convex normed spaces

Lei Li

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We study the extension property of isometries on the unit sphere of the $\ell^{1}$-sum of strictly normed spaces, which is a special case of Tingley’s isometric extension problem. In this paper, we will give some sufficient conditions such that such isometries can be extended to the whole space.

Article information

Ann. Funct. Anal. Volume 7, Number 1 (2016), 33-41.

Received: 4 March 2015
Accepted: 23 April 2015
First available in Project Euclid: 6 November 2015

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Mathematical Reviews number (MathSciNet)

Primary: 46B04: Isometric theory of Banach spaces
Secondary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

isometries unit spheres strictly convex spaces


Li, Lei. Isometries on the unit sphere of the ℓ 1 -sum of strictly convex normed spaces. Ann. Funct. Anal. 7 (2016), no. 1, 33--41. doi:10.1215/20088752-3163452.

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