The geometry of flat Banach spaces

Harrell, R. E.; Karlovitz, L. A.

doi:10.1090/S0002-9947-1974-0338737-4

The geometry of flat Banach spaces
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by R. E. Harrell and L. A. Karlovitz PDF

Trans. Amer. Math. Soc. 192 (1974), 209-218 Request permission

Abstract:

A Banach space is flat if the girth of its unit ball is 4 and if the girth is achieved by some curve. (Equivalently, its unit ball can be circumnavigated along a centrally symmetric path whose length is 4.) Some basic geometric properties of flat Banach spaces are given. In particular, the term flat is justified.

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Zur Theorie abstrakter Funktionen

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R. E. Harrell and L. A. Karlovitz, Girths and flat Banach spaces, Bull. Amer. Math. Soc. 76 (1970), 1288–1291. MR 267383, DOI 10.1090/S0002-9904-1970-12643-X

Characterization of flat Banach spaces

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