Factorization and domination of positive Banach–Saks operators
Tom 189 / 2008
Studia Mathematica 189 (2008), 91-101 MSC: 46B42, 47B65, 47B07. DOI: 10.4064/sm189-1-7
It is proved that every positive Banach–Saks operator $T:E\rightarrow F$ between Banach lattices $E$ and $F$ factors through a Banach lattice with the Banach–Saks property, provided that $F$ has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds–Fremlin sense, are obtained for the class of Banach–Saks operators.