(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

for L, M: V -> W, L, M, linear let||L|| = sup{|L(v)|: v in V, |v| <= 1}

show ||L + M|| < ||L|| + ||M||

2. Relevant equations

3. The attempt at a solution

so is it true that if |L(x) + M(x)| defines a sup for L + M (x for which |L(x) + M(x)| is the sup), then it also defines a sup for L and sup for M, as L and M are both defined on V? im getting caught up on this and im thinking maybe theres a simpler way, i.e., either defining sets and using the standard results for sup on sets, or to exploit the linearity in a clever way

think im overlooking something simple

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: ||L||, transformations

**Physics Forums | Science Articles, Homework Help, Discussion**