Some classes of Banach spaces and complemented subspaces of operators

Ghenciu, Ioana

doi:10.15352/aot.1802-1318

Cited by 16 publications

(11 citation statements)

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“…The following result appeared in [19]. Here, we include a new proof for the convenience of the reader.…”

Section: P-sequentially Right and P-sequentially Right * Properties Omentioning

confidence: 95%

“…Hence, (x ⊗ y n ) n is p-Right null in X π Y and so, the equivalence between (i) and (v) in ( [19,Theorem 3.26]) implies that {T n (x) : n ∈ N} is a p-Right set in Y * . Therefore, {T n (x) : n ∈ N} is relatively weakly compact.…”

Section: P-sequentially Right and P-sequentially Right * Properties Omentioning

confidence: 99%

“…For more information and examples of those spaces with the sequentially Right property and sequentially Right * property, we refer to [8,17,21,26]. Recently, Ghenciu [19], by introducing the concepts of Dunford-Pettis p-convergent operators, p-Right sets and p-sequentially Right property obtained some characterizations of these notions. Numerous authors, by studying localized properties, e.g., (V)-sets, (V * )-sets, Dunford-Pettis sets, (L)-sets, point evaluations sets and Right sets, showed how these notions can be used to study more global structure properties.…”

Section: Introductionmentioning

confidence: 99%

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Sequentially right-like properties on Banach spaces

Alikhani

2019

Filomat

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In this paper, we study first the concept of p-sequentially Right property, which is p-version of the sequentially Right property. Also, we introduce a new class of subsets of Banach spaces which is called p-Right * set and obtain the relationship between p-Right subsets and p-Right * subsets of dual spaces. Furthermore, for 1 ≤ p < q ≤ ∞, we introduce the concepts of properties (SR) p,q and (SR *) p,q in order to find a condition such that every Dunford-Pettis q-convergent operator is Dunford-Pettis p-convergent. Finally, we apply these concepts and obtain some characterizations of the p-Dunford-Pettis relatively compact property of Banach spaces and their dual spaces.

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“…The following result appeared in [19]. Here, we include a new proof for the convenience of the reader.…”

Section: P-sequentially Right and P-sequentially Right * Properties Omentioning

confidence: 95%

Section: P-sequentially Right and P-sequentially Right * Properties Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sequentially right-like properties on Banach spaces

Alikhani

2019

Filomat

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“…A sequence (x n ) n in X is said to be weakly p-convergent to x ∈ X if (x n − x) n ∈ ℓ w p (X). Recently, the concepts of Dunford-Pettis p-convergent operators between Banach spaces and p-Dunford-Pettis relatively compact property on Banach spaces was introduced by Ghenciu [20] as follows:…”

Section: Introductionmentioning

confidence: 99%

A Study on Dunford–Pettis Completely Continuous Like Operators

Alikhani

2019

Iran J Sci Technol Trans Sci

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In this article, the class of all Dunford-Pettis p-convergent operators and p-Dunford-Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces X and Y such that the class of bounded linear operators from X to Y and some its subspaces have the p-Dunford-Pettis relatively compact property. In addition, if Ω is a compact Hausdorff space, then we prove that dominated operators from the space of all continuous functions from K to Banach space X (in short C(Ω, X)) taking values in a Banach space with the p-(DP rcP ) are p-convergent when X has the Dunford-Pettis property of order p. Furthermore, we show that if T : C(Ω, X) → Y is a strongly bounded operator with representing measure m : Σ → L(X, Y ) andT : B(Ω, X) → Y is its extension, then T is Dunford-Pettis p-convergent if and only ifT is Dunford-Pettis p-convergent.Mathematics Subject Classification (2010). 46B20, 46B25,46B28.

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“…• A Banach space X has the (SR) property if and only if it has the (L)-Dunford-Pettis property. Recently, Ghenciu [23] introduced the concepts of Dunford-Pettis p-convergent operators, p-Dunford-Pettis relatively compact property (in short p-(DP rcP )), p-Right sets and psequentially Right property ( in short p-(SR)) as follows:…”

Section: Introductionmentioning

confidence: 99%

On pseudo weakly compact operators of order $ P$

Alikhani

2018

Preprint

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In this paper, we introduce the concept of a pseudo weakly compact operator of order p between Banach spaces. Also we study the notion of p-Dunford-Pettis relatively compact property which is in "general" weaker than the Dunford-Pettis relatively compact property and gives some characterizations of Banach spaces which have this property. Moreover, by using the notion of p-Right subsets of a dual Banach space, we study the concepts of p-sequentially Right and weak p-sequentially Right properties on Banach spaces. Furthermore, we obtain some suitable conditions on Banach spaces X and Y such that projective tensor and injective tensor products between X and Y have the p-sequentially Right property. Finally, we introduce two properties for the Banach spaces, namely p-sequentially Right * and weak p-sequentially Right * properties and obtain some characterizations of these properties.

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Some classes of Banach spaces and complemented subspaces of operators

Cited by 16 publications

References 0 publications

Sequentially right-like properties on Banach spaces

Sequentially right-like properties on Banach spaces

A Study on Dunford–Pettis Completely Continuous Like Operators

On pseudo weakly compact operators of order $ P$

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