$\varepsilon$-Isometries of convex bodies in $l^n_\infty$ and $l^n_1$

Igor A. Vestfrid

doi:10.3842/umzh.v76i9.8295

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 $\varepsilon$-isometry of a convex body in $l^n_\infty$ or in $l^n_1$ can be well approximated by an affine surjective isometry.

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