On the sum of a narrow and a compact operators
Copyright policy )On the sum of a narrow and a compact operators
Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm. It is proved that for every Köthe $F$-space $X$ and for every locally convex $F$-space $Y$ the sum $T_1+T_2$ of a narrow operator $T_1:X\to Y$ and a compact narrow operator $T_2:X\to Y$ is a narrow operator. This gives a positive answers to questions asked by M.~Popov and B.~Randrianantoanina (\cite[Problem 5.6 and Problem 11.63]{PR})
- Chernivtsi National University Ukraine
Banach lattices, General Topology (math.GN), Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, narrow operators, Linear operators on function spaces (general), Linear operators defined by compactness properties, FOS: Mathematics, Ordered topological linear spaces, vector lattices, compact operators, Mathematics - General Topology
Banach lattices, General Topology (math.GN), Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, narrow operators, Linear operators on function spaces (general), Linear operators defined by compactness properties, FOS: Mathematics, Ordered topological linear spaces, vector lattices, compact operators, Mathematics - General Topology
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