Abstract
Let E, F be Banach lattices, where E has the disjoint Riesz decomposition property. For a lattice homomorphism \(T:E\rightarrow F\) and a bounded subset A of E, we establish a necessary and sufficient condition under which TA is b-order bounded. Based on this, we study the b-order boundedness of subsets of E and obtain several characterizations of AM-spaces. Furthermore, we introduce and investigate a novel type of operators referred to as M-serially summing operator. The connections of this category of operators with classical notions of operators, such as majorizing operators, preregular operators and serially summing operators, are considered.
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Communicated by Denny Leung.
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Zhang, F., Shen, H. & Chen, Z. M-serially summing operators on Banach lattices. Ann. Funct. Anal. 15, 29 (2024). https://doi.org/10.1007/s43034-024-00331-2
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DOI: https://doi.org/10.1007/s43034-024-00331-2
Keywords
- AM-space
- b-Order bounded set
- Preregular operator
- Serially summing operator
- M-serially summing operator
- Disjoint Riesz decomposition property