theorem Th37: :: DUALSP01:31

for X being RealNormSpace
for f, g being Point of (DualSp X)
for a being Real holds
( ( ||.f.|| = 0 implies f = 0. (DualSp X) ) & ( f = 0. (DualSp X) implies ||.f.|| = 0 ) & ||.(a * f).|| = |.a.| * ||.f.|| & ||.(f + g).|| <= ||.f.|| + ||.g.|| )