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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1446819347

Digital Object Identifier
doi:10.1215/20088752-3163452

Mathematical Reviews number (MathSciNet)
MR3449338

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

Keywords
isometries unit spheres strictly convex spaces

Citation

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. https://projecteuclid.org/euclid.afa/1446819347


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References

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