Math Help - two problems about invariant subspace problem

1. 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...

2. Re: two problems about invariant subspace problem

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

3. Re: two problems about invariant subspace problem

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.