Banach spaces in which Dunford-Pettis sets are relatively compact

Emmanuele, Giovanni

doi:10.1007/bf01190118

Cited by 46 publications

(36 citation statements)

References 10 publications

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“…By Corollary 2.5 it follows that E ⊗ π F has the DPP. Similar arguments to those given in the proof of Theorem 2.4 (b) ⇒ a)) show that L(E, F * ) = K(E, F * ) and hence, by [17], E ⊗ π F does not contain 1 . Therefore, by [16, Theorem 3], we conclude that E ⊗ π F * has the Schur property.…”

Section: And the Banach Space B(h K) Of All Bounded Linear Operatorsmentioning

confidence: 61%

The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

Guerrero

Peralta

2005

Math. Z.

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Section: And the Banach Space B(h K) Of All Bounded Linear Operatorsmentioning

confidence: 61%

The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

Guerrero

Peralta

2005

Math. Z.

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“…(iv) It is known that ℓ 1 [X] is isometrically isomorphic to K(c 0 , X) (see [11]). Since X has the (RDP * P ) p and c * 0 = ℓ 1 has the Schur property.…”

Section: Resultsmentioning

confidence: 99%

A study of reciprocal Dunford–Pettis-like properties on Banach spaces

Alikhani

2019

Adv. Oper. Theory

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In this article, we study the relationship between p-(V ) subsets and p-(V * ) subsets of dual spaces. We investigate the Banach space X with the property that adjoint every p-convergent operator T : X → Y is weakly q-compact, for every Banach space Y. Moreover, we define the notion of qreciprocal Dunford-Pettis * property of order p on Banach spaces and obtain a characterization of Banach spaces with this property. Also, the stability of reciprocal Dunford-Pettis property of order p for projective tensor product is given.2010 Mathematics Subject Classification. Primary 46B20; Secondary 46B25, 46B28. Key words and phrases. p-convergent operators, reciprocal Dunford-Pettis property and Dunford-Pettis property of order p..

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“…But in general the converse is not true. The concept of Dunford-Pettis relatively compact property (briefly denoted by (DP rcP )) on Banach spaces was introduced by Emmanuele [16]. A Banach space X has the (DP rcP ), if every Dunford-Pettis subset of X is relatively compact.…”

Section: Introductionmentioning

confidence: 99%

“…A Banach space X has the (DP rcP ), if every Dunford-Pettis subset of X is relatively compact. It is well known that any dominated operator from C(Ω, X) spaces taking values in a Banach space with the (DP rcP ) is completely continuous when X has the Dunford-Pettis property (see [16]). Wen and Chen [24], introduced the definition of a Dunford-Pettis completely continuous operator in order to characterize the (DP rcP ) on Banach spaces.…”

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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Banach spaces in which Dunford-Pettis sets are relatively compact

Cited by 46 publications

References 10 publications

The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

A study of reciprocal Dunford–Pettis-like properties on Banach spaces

A Study on Dunford–Pettis Completely Continuous Like Operators

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