two problems about invariant subspace problem

1)Give an example of invariant subspace which is not compact friendly.

2)Prove that lp spaces are discrete Banach lattice. p>=1

Thanks...

Can you define the terms "compact friendly" and "discrete Banach lattice"?

A positive operator B on E is said to be compact-friendly if there is a positive operator that commutes with B and dominates a non-zero operator which is dominated by a compact positive operator.