During the last few years the authors have studied extensively the invariant subspace problem of positive operators; see  for a survey of this investigation. In  the authors introduced the class of compact-friendly operators and proved for them a general theorem on the existence of invariant subspaces. It was then asked if every positive operator is compact-friendly. In this note, we present an example of a positive operator which is not compact-friendly but which, nevertheless, has a non-trivial closed invariant subspace.
Positivity – Springer Journals
Published: Oct 14, 2004
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