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for ''x'' and ''y'' in ''D''.
If the diameter of ''D'' is less than ''R'' then, by taking suitable holomorphic functions ''g'' of the form
:<math>\displaystyle{g(z)=a(z) + b}</math>
with ''a'' in ''X''* and ''b'' in '''C''', it follows that
:<math>\displaystyle{\alpha(z,v)\ge \|v\|/R,}</math>
and hence that
:<math>\displaystyle{d(x,y)\ge \|x-y\|/R.}</math>
In particular ''d'' defines a metric on ''D''.
==References==
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