A new geometric property of the unit sphere of a normed space. (Italian. English summary) Zbl 0633.46019
We define the T-spaces among the real Banach spaces. This class includes finite dimensional and uniformly smooth spaces. We discuss some classical Banach spaces with respect to the T-property and related properties. We prove some properties of the T-spaces concerning Lipschitz self maps of the unit ball of the space.
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 46B03 | Isomorphic theory (including renorming) of Banach spaces |
Keywords:
T-spaces; real Banach spaces; uniformly smooth spaces; Lipschitz self maps of the unit ballReferences:
| [1] | Benyamini, Y.; Sternfeld, Y., Spheres in infinite-dimensional normed spaces are Lipschitz contractible, Proc. Amer. Math. Soc., 88, 439-445 (1983) · Zbl 0518.46010 · doi:10.2307/2044990 |
| [2] | Franchetti, C., Lipschitz maps on the unit ball of normed spaces, Conf. Semin. Matem. Univers. Bari, 202, 1-11 (1985) · Zbl 0576.46007 |
| [3] | C. Franchetti,Lipschitz maps and the geometry of the unit ball in normed spaces, Archiv der Mathematik (1985). · Zbl 0576.46007 |
| [4] | Goebel, K., On the minimal displacement of points under Lipschitzian mappings, Pacific J. Math., 45, 151-163 (1973) · Zbl 0265.47046 |
| [5] | R. B. Holmes,A course on optimization and best approximation, Springer LNM 257 (1972). · Zbl 0235.41016 |
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