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Mar
18
comment $2$-normed Spaces
I think that the formula at the end of the first page of the paper you mention also makes sense in bornological vector spaces. In stead of taking the sup over F_L, the sup has to run over all functionals whose absolute value is bounded by 1 on a fixed bounded set. If this is indeed the case, every bornological space that is not a normed space gives an example as you want.
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