Sequentially right-like properties on Banach spaces

Alikhani, M.

doi:10.2298/fil1914461a

Cited by 4 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular if K ⊂ X * , we answer this question. Indeed, we obtain a characterization for those Banach spaces in which p-(DP L) sets are q-(DP L) (see Definition 4.1 and Theorem 4.4 in [2]). (ii) Proposition 3.1 assertion (iii) implies that every relatively weakly compact subset of a topological dual Banach space is p-(DP L), while the converse of this implication is false.…”

Section: Resultsmentioning

confidence: 99%

Factorization Theorem through a Dunford-Pettis $p$-convergent operator

Alikhani¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In this article, we introduce the notion of p-(DP L) sets. Also, a factorization result for differentiable mappings through Dunford-Pettis p-convergent operators is investigated. Namely, if X, Y are real Banach spaces and U is an open convex subset of X, then we obtain that, given a differentiable mapping f : U → Y its derivative f ′ takes U -bounded sets into p-(DP L) sets if and only if it happens f = g • S, where S is a Dunford-Pettis p-convergent operator from X into a suitable Banach space Z and g : S(U ) → Y is a Gâteaux differentiable mapping with some additional properties.

show abstract

Section: Resultsmentioning

confidence: 99%

Factorization Theorem through a Dunford-Pettis $p$-convergent operator

Alikhani¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Some applications of p-(DPL) sets

Alikhani

2023

Filomat

View full text Add to dashboard Cite

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 Fr?chet differentiable and f? takes bounded sets into p-(DPL) sets if and only if f may be written in the form f = 1?S where the intermediate space is normed, S is a Dunford-Pettis p-convergent operator, and g is a G?teaux differentiable mapping with some additional properties.

show abstract

A note on some classes of operators on C(K,X)

Ghenciu

Popescu

2023

Quaestiones Mathematicae

View full text Add to dashboard Cite

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, Σ is the σ-algebra of Borel subsets of K, C(K, X) is the Banach space of all continuous X-valued functions (with the supremum norm), and T : C(K, X) → Y is a strongly bounded operator with representing measure m : Σ → L(X, Y ).We show that if T : B(K, X) → Y is its extension, then T is weak Dunford-Pettis (resp. weak * Dunford-Pettis, weak p-convergent, weak * p-convergent) if and only if T has the same property.We prove that if T : C(K, X) → Y is strongly bounded limited completely continuous (resp. limited p-convergent), then m(A) : X → Y is limited completely continuous (resp. limited p-convergent) for each A ∈ Σ. We also prove that the above implications become equivalences when K is a dispersed compact Hausdorff space.

show abstract

Sequentially right-like properties on Banach spaces

Cited by 4 publications

References 15 publications

Factorization Theorem through a Dunford-Pettis $p$-convergent operator

Factorization Theorem through a Dunford-Pettis $p$-convergent operator

Some applications of p-(DPL) sets

A note on some classes of operators on C(K,X)

Contact Info

Product

Resources

About