- #1
j0k3R_
- 11
- 0
Homework Statement
for L, M: V -> W, L, M, linear let||L|| = sup{|L(v)|: v in V, |v| <= 1}
show ||L + M|| < ||L|| + ||M||
Homework Equations
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? I am getting caught up on this and I am thinking maybe there's 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 I am overlooking something simple