Some isomorphic properties in $K(X,Y)$ and in projective tensor products

Cilia, Raffaella; Emmanuele, Giovanni

doi:10.4064/cm6184-12-2015

Cited by 10 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our aim in this section is to obtain some suitable conditions on X and Y such that any dominated operator T from C(Ω, X) into Y is p-convergent. Recall that, the authors in [9,19] by using Right topology, independently, proved that a sequence (x n ) n in a Banach space X is Right null if and only if it is Dunford-Pettis and weakly null. Also, they showed that a sequence (x n ) n in a Banach space X is Right Cauchy if and only if it is Dunford-Pettis and weakly Cauchy.…”

Section: Dunford-pettis Relatively Compact Property Of Order Pmentioning

confidence: 99%

A Study on Dunford–Pettis Completely Continuous Like Operators

Alikhani

2019

Iran J Sci Technol Trans Sci

View full text Add to dashboard Cite

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.

show abstract

Section: Dunford-pettis Relatively Compact Property Of Order Pmentioning

confidence: 99%

A Study on Dunford–Pettis Completely Continuous Like Operators

Alikhani

2019

Iran J Sci Technol Trans Sci

View full text Add to dashboard Cite

show abstract

“…Later on Kacena [21], by introducing the notion of Right set in the dual of X, gave a characterization of those Banach spaces which have the sequentially Right property. Recently, Cilia and Emmanuele [8] and Ghenciu [18], obtained some sufficient conditions implying that the projective tensor product of two Banach spaces has the sequentially Right property. Moreover, they introduced the concept sequentially Right * property on Banach spaces and gave its characterization.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, they introduced the concept sequentially Right * property on Banach spaces and gave its characterization. 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.…”

Section: Introductionmentioning

confidence: 99%

“…The relationship between (L) subsets and Dunford-Pettis subsets of dual spaces was obtained by Bator et al [3]. Recently, the authors [8,18], by using Right topology, proved that a sequence (x n ) n in a Banach space X is Right null if and only if it is Dunford-Pettis and weakly null. Also, they showed that a sequence (x n ) n in a Banach space X is Right Cauchy if and only if it is Dunford-Pettis and weakly Cauchy.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sequentially right-like properties on Banach spaces

Alikhani

2019

Filomat

View full text Add to dashboard Cite

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.

show abstract

“…A Banach space X has the (L)-Dunford-Pettis property, if every (L)-Dunford-Pettis subset of X * is relatively weakly compact. Recently, Cilia and Emmanuele in [8] and Ghenciu in [22] obtained a characterization for Right null sequences. In fact, they showed that a sequence (x n ) n in a Banach space X is Right null if and only if it is Dunford-Pettis and weakly null.…”

Section: Introductionmentioning

confidence: 99%

On pseudo weakly compact operators of order $ P$

Alikhani

2018

Preprint

View full text Add to dashboard Cite

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.

show abstract

Some isomorphic properties in $K(X,Y)$ and in projective tensor products

Cited by 10 publications

References 20 publications

A Study on Dunford–Pettis Completely Continuous Like Operators

A Study on Dunford–Pettis Completely Continuous Like Operators

Sequentially right-like properties on Banach spaces

On pseudo weakly compact operators of order $ P$

Contact Info

Product

Resources

About