Wide operators on Kothe function spaces
Chernivtsi National University
We study operators defined on Kothe function spaces which are uniformly bounded from below at some sign functions supported on any fixed measurable set. Precise definition is a kind of opposite to the definition of narrow operators, so many questions concerning the relationship between narrow and wide operators naturally arise. The main questions are to describe how "large" has to be a wide operator, and how "small" has to be an operator which is "nowhere" wide. Some easy to formulate problems on wide operators turn out to be more involved than their analogues for narrow operators, and most of the results have restrictive assumptions on the domain spaces. We pose some open problems.
vector lattice; orthogonally additive operator; disjointness preserving operator
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