ε-Isometries of convex bodies in ln and ln1

Authors

  • Igor A. Vestfrid Haifa, Israel

DOI:

https://doi.org/10.3842/umzh.v76i9.8295

Keywords:

\varepsilon--isometry, isometric approximation, classical Banach spaces, stability

Abstract

UDC 517.5

It is shown that every ε-isometry of a convex body in ln or in ln1 can be well approximated by an affine surjective isometry.

References

Y. Benyamini, J. Lindenstrauss, Geometric nonlinear functional analysis, vol. 1, Colloquium Publication, 48, Amer. Math. Soc., Providence, RI (2000). DOI: https://doi.org/10.1090/coll/048

Th. M. Rassias, Properties of isometries and approximate isometries. Recent progress in inequalities (Niš, 1996), Math. Appl., 430, Kluwer Acad. Publ., Dordrecht (1998), p. 341–379. DOI: https://doi.org/10.1007/978-94-015-9086-0_19

Th. M. Rassias, Properties of isometric mappings, J. Math. Anal. and Appl., 235, 108–121 (1999). DOI: https://doi.org/10.1006/jmaa.1999.6363

I. A. Vestfrid, ε-isometries in Euclidean spaces, Nonlinear Anal., 63, 1191–1198 (2005). DOI: https://doi.org/10.1016/j.na.2005.05.036

I. A. Vestfrid, Addendum to``ε-Isometries in Euclidean spaces, [Nonlinear Anal., 63, 1191–1198 (2005)], Nonlinear Anal., 67, 1306–1307 (2007). DOI: https://doi.org/10.1016/j.na.2006.06.053

I. A. Vestfrid, ε-Isometries in l^n_∞, Nonlinear Funct. Anal. and Appl., 12, 433–438 (2007).

I. A. Vestfrid, ε-Isometries in l^n_1, Aequat. Math. (2024); https://doi.org/10.1007/s00010-023-01023-3. DOI: https://doi.org/10.1007/s00010-023-01023-3

Published

30.09.2024

Issue

Section

Short communications

How to Cite

Vestfrid, Igor A. “\varepsilon-Isometries of Convex Bodies in l^n_\infty and l^n_1”. Ukrains’kyi Matematychnyi Zhurnal, vol. 76, no. 9, Sept. 2024, pp. 1419-23, https://doi.org/10.3842/umzh.v76i9.8295.