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- W3122659267 abstract "In this article we investigate the disjointly non-singular (DNS) operators. Following [8] we say that an operator $T$ from a Banach lattice $F$ into a Banach space $E$ is DNS, if no restriction of $T$ to a subspace generated by a disjoint sequence is strictly singular. We partially answer a question from [8] by showing that this class of operators forms an open subset of $Lleft(F,Eright)$ as soon as $F$ is order continuous. Moreover, we show that in this case $T$ is DNS if and only if the norm topology is the minimal topology which is simultaneously stronger than the unbounded norm topology and the topology generated by $T$ as a map (we say that $T$ complements the unbounded norm topology in $F$). Since the class of DNS operators plays a similar role in the category of Banach lattices as the upper semi-Fredholm operators play in the category of Banach spaces, we investigate and indeed uncover a similar characterization of the latter class of operators, but this time they have to complement the weak topology." @default.
- W3122659267 created "2021-02-01" @default.
- W3122659267 creator A5083758248 @default.
- W3122659267 date "2021-01-17" @default.
- W3122659267 modified "2023-09-27" @default.
- W3122659267 title "Disjointly non-singular operators on order continuous Banach lattices complement the unbounded norm topology" @default.
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