On Banach spaces whose dual balls are not weak∗ sequentially compact

Hagler, James N.; Johnson, William B.

doi:10.1007/bf02760638

Cited by 58 publications

(36 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, suppose not. Then also E would be m-measurable, so by 23 for all x E A. It is easily seen that ${E) is not Lebesgue-measurable, where E is as above.…”

Section: A Compact Subset Of B X (X) Is Sequentially Compactmentioning

confidence: 99%

Some recent discoveries in the isomorphic theory of Banach spaces

Rosenthal¹

1978

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

“…Indeed, suppose not. Then also E would be m-measurable, so by 23 for all x E A. It is easily seen that ${E) is not Lebesgue-measurable, where E is as above.…”

Section: A Compact Subset Of B X (X) Is Sequentially Compactmentioning

confidence: 99%

Some recent discoveries in the isomorphic theory of Banach spaces

Rosenthal¹

1978

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

“…[10] (see also [7]) that B E * is weak * -sequentially compact. Hence if (e * n ) is any sequence in B E * , there is a subsequence (f * n ) so that T * f * n is weak * and hence weakly convergent in X * .…”

Section: Theorem 25 Suppose X Is a Subspace Of An L-embedded Banachmentioning

confidence: 93%

The range of operators on von Neumann algebras

Bermúdez

Kalton

2001

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…also [19]) Godefroy's boundary problem is answered in the affirmative yielding a new proof of James's theorem based on Simon's inequality, Rosenthal's ℓ 1 -theorem [23] and a refinement of a technique due to J. Hagler and W. B. Johnson [8] for extracting ℓ 1 -sequences in spaces whose duals contain ℓ 1 -sequences without w * -convergent subsequences. The proof of James's theorem given in [16] was the first one to combine the results from [24], [23] and [8]. We finally mention paper [2] where the arguments of [20] are extended to give quantitative versions of James's theorem.…”

Section: Introductionmentioning

confidence: 99%

An extension of James's compactness theorem

Gasparis

2015

Journal of Functional Analysis

View full text Add to dashboard Cite

Abstract. Let X and Y be Banach spaces and F ⊂ BY * . Endow Y with the topology τF of point-wise convergence on F . Assume that T : X * → Y is a bounded linear operator which is (w * , τF ) continuous. Assume further that every vector in the range of T attains its norm at some element of F (that is, for every x * ∈ X * there exists y * ∈ F such that T (x * ) = |y * (T x * )|). Then T is (w * , w) continuous. The proof relies on Rosenthal's ℓ1-theorem. As a corollary to the above result, one obtains an alternative proof of James's compactness theorem that a bounded subset K of a Banach space E is relatively weakly compact provided that each functional in E * attains its supremum on K.

show abstract

On Banach spaces whose dual balls are not weak∗ sequentially compact

Cited by 58 publications

References 6 publications

Some recent discoveries in the isomorphic theory of Banach spaces

Some recent discoveries in the isomorphic theory of Banach spaces

The range of operators on von Neumann algebras

An extension of James's compactness theorem

Contact Info

Product

Resources

About