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A geometrically aberrant Banach space with uniformly normal structure. (English) Zbl 0646.46017
The author gives an equivalent norm \(\| \cdot \|_ a\) on \((\ell_ 2,\| \cdot \|_ 2)\) such that \((\ell_ 2,\| \cdot \|_ a)\) is non-URED, non-LUR, non-wUKK and non-KUR, but \((\ell_ 2,\| \cdot \|_ a)\) has uniformly normal structure.
Reviewer: Liu Zheng

MSC:
46B20 Geometry and structure of normed linear spaces
47H10 Fixed-point theorems
46B25 Classical Banach spaces in the general theory
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References:
[1] Day, Normed Linear Spaces (1973) · doi:10.1007/978-3-662-09000-8
[2] DOI: 10.1307/mmj/1029001259 · Zbl 0275.46016 · doi:10.1307/mmj/1029001259
[3] DOI: 10.2307/2045028 · Zbl 0512.46012 · doi:10.2307/2045028
[4] Sullivan, Canad. J. Math. 31 pp 628– (1979) · Zbl 0422.46011 · doi:10.4153/CJM-1979-063-9
[5] Giles, Bull. Aust. Math. Soc. 31 pp 75– (1985)
[6] Maluta, Pacific J. Math 110 pp 126– (1984)
[7] Lin, On the uniformly normal structure (1985)
[8] Huff, Rocky Mountains J. of Math. 10 pp 743– (1980)
[9] Kirk, Proc. of Research Workshop of Banach spaces theory pp 113– (1981)
[10] Xin tai, KUR spaces are NUC spaces pp 1473– (1983)
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