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Transactions of the American Mathematical Society

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The geometry of flat Banach spaces


Authors: R. E. Harrell and L. A. Karlovitz
Journal: Trans. Amer. Math. Soc. 192 (1974), 209-218
MSC: Primary 46B05
DOI: https://doi.org/10.1090/S0002-9947-1974-0338737-4
MathSciNet review: 0338737
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0338737-4
Article copyright: © Copyright 1974 American Mathematical Society

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