Almost Weakly Compact Operators

Ghenciu, Ioana; Lewis, Paul W.

doi:10.4064/ba54-3-6

Cited by 19 publications

(15 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, H * (y * ) := {T * (y * ) : T ∈ H} is a p-Right subset of X, hence relatively weakly compact. Then, by ( [14,Theorem 4. 8]), H is relatively weakly compact.…”

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

confidence: 93%

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

“…Therefore, H * (y * ) := {T * (y * ) : T ∈ H} is a p-Right subset of X, hence relatively weakly compact. Then, by ( [14,Theorem 4. 8]), H is relatively weakly compact.…”

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

confidence: 93%

Sequentially right-like properties on Banach spaces

Alikhani

2019

Filomat

View full text Add to dashboard Cite

show abstract

“…The following theorem was proved in [13]. Theorem 1.14 implies that every operator T : Y → X with completely continuous adjoint is weakly precompact.…”

Section: Proposition 113mentioning

confidence: 99%

Limited Sets and Bibasic Sequences

Ghenciu¹

2015

Can. math. bull.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [20,Corollary 4.11] it was shown that if L w * (X * , Y ) = K w * (X * , Y ) and both X and Y have the BD property, then K w * (X * , Y ) has the BD property. In [23,Theorem 2] it was shown that if X has the wGP property and the Gelfand-Phillips property and Y has the wGP property, then K w * (X * , Y ) has the wGP property.…”

Section: Introductionmentioning

confidence: 99%