- #1

- 346

- 23

- 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

p-norm's definition.

Dear everyone,

I am having trouble with this problem. I have convinced myself that the ##a^t-a\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 p-norm is less or equal to the q-norm.

Thanks,

Cbarker1

I am having trouble with this problem. I have convinced myself that the ##a^t-a\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 p-norm is less or equal to the q-norm.

Thanks,

Cbarker1