Geodesic
Some applications of p-(DPL) sets
Filomat, Tome 37 (2023) no. 5, p. 1367

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DOI

In this paper, we introduce a new class of subsets of class bounded linear operators between Banach spaces which is called p-(DPL) sets. Then, the relationship between these sets with equicompact sets is investigated. Moreover, we define p-version of Right sequentially continuous differentiable mappings and get some characterizations of these mappings. Finally, we prove that a mapping f : X → Y between real Banach spaces is Fréchet differentiable and f ′ takes bounded sets into p-(DPL) sets if and only if f may be written in the form f = • S where the intermediate space is normed, S is a Dunford-Pettis p-convergent operator, and g is a Gáteaux differentiable mapping with some additional properties.
DOI : 10.2298/FIL2305367A
Classification : 46B25, 46G05
Keywords: Dunford-Pettis property of order p, Dunford-Pettis p-convergent operators, Right sequentially continuous 
Morteza Alikhani. Some applications of p-(DPL) sets. Filomat, Tome 37 (2023) no. 5, p. 1367 . doi: 10.2298/FIL2305367A
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     title = {Some applications of {p-(DPL)} sets},
     journal = {Filomat},
     pages = {1367 },
     year = {2023},
     volume = {37},
     number = {5},
     doi = {10.2298/FIL2305367A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305367A/}
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