 #1
cbarker1
Gold Member
MHB
 340
 21
 Homework Statement:
 Prove that l^p is a subset of l^q for all p,q from 1 to infinity. Then prove it is strict subset. First, prove that a^t<=a for all t,a in (0,1]. Then prove that finite sum of x_i^t<= the sum of xi.
 Relevant Equations:

a^t<=a for all a,t
pnorm's definition.
Dear everyone,
I am having trouble with this problem. I have convinced myself that the ##a^ta\leq 0## is true. Now, I am trying to applying this inequality for the finite series and I don't know where to start. After that, proving that the pnorm is less or equal to the qnorm.
Thanks,
Cbarker1
I am having trouble with this problem. I have convinced myself that the ##a^ta\leq 0## is true. Now, I am trying to applying this inequality for the finite series and I don't know where to start. After that, proving that the pnorm is less or equal to the qnorm.
Thanks,
Cbarker1