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

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

Thanks...

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- Apr 27th 2012, 02:12 PMmamitwo 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... - Apr 28th 2012, 02:37 AMgirdavRe: two problems about invariant subspace problem
Can you define the terms "compact friendly" and "discrete Banach lattice"?

- Apr 28th 2012, 09:17 AMmamiRe: 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.