turkmath.org

The celebrated result of Victor Lomonosov on the existence of non-trivial closed hyperinvariant subspaces for compact Banach space operators gave rise to the introduction of a new notion in the area of positivity, that of compact-friendliness, which motivated a huge amount of research pertaining to the invariant subspace problem for positive operators on Banach lattices. The talk aims to survey these results in connection with the ones obtained during the past three years in collaboration with Tunç Mısırlıoğlu of İstanbul Kültür University.