scholarly journals Continuous images of weakly compact subsets of Banach spaces

1977 ◽  
Vol 70 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Yoav Benyamini ◽  
Mary Ellen Rudin ◽  
Michael Wage
Keyword(s):  
Banach Spaces ◽  
Weakly Compact ◽  
Continuous Images ◽  
Compact Subsets

scholarly journals On two problems concerning Eberlein compacta

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Witold Marciszewski
Keyword(s):  
Banach Spaces ◽  
Compact Space ◽  
Dimensional Subspace ◽  
Weakly Compact ◽  
Compact Spaces ◽  
Eberlein Compact ◽  
Continuous Images

AbstractWe discuss two problems concerning the class Eberlein compacta, i.e., weakly compact subspaces of Banach spaces. The first one deals with preservation of some classes of scattered Eberlein compacta under continuous images. The second one concerns the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. We show that the existence of such Eberlein compacta is consistent with . We also show that it is consistent with that each Eberlein compact space of weight $$> \omega _1$$ > ω 1 contains a nonmetrizable closed zero-dimensional subspace.

scholarly journals On weakly compact subsets of Banach spaces

1966 ◽  
Vol 17 (2) ◽  
pp. 407-407 ◽  
Author(s):  
H. H. Corson ◽  
J. Lindenstrauss
Keyword(s):  
Banach Spaces ◽  
Weakly Compact ◽  
Compact Subsets

scholarly journals The strongWCDproperty for Banach spaces

1995 ◽  
Vol 18 (1) ◽  
pp. 67-70
Author(s):  
Dave Wilkins
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Property A ◽  
Weakly Compact ◽  
Compact Structure ◽  
Structure Theorems ◽  
Compact Subsets

In this paper, we introduce weakly compact version of the weakly countably determined (WCD) property, the strongWCD(SWCD) property. A Banach spaceXis said to beSWCDif there s a sequence (An) of weak∗compact subsets ofX∗∗such that ifK⊂Xis weakly compact, there is an(nm)⊂Nsuch thatK⊂⋂m=1∞Anm⊂X. In this case, (An) is called a strongly determining sequence forX. We show thatSWCG⇒SWCDand that the converse does not hold in general. In fact,Xis a separableSWCDspace if and only if (X, weak) is anℵ0-space. Usingc0for an example, we show how weakly compact structure theorems may be used to construct strongly determining sequences.

Weakly compactly generated locally convex spaces

1977 ◽  
Vol 82 (1) ◽  
pp. 85-98 ◽  
Author(s):  
Richard J. Hunter ◽  
John Lloyd
Keyword(s):  
Banach Spaces ◽  
Compact Subset ◽  
Locally Convex Spaces ◽  
Weakly Compact ◽  
Permanence Properties ◽  
Locally Convex ◽  
Compactly Generated ◽  
Convex Spaces ◽  
Compact Subsets

AbstractLocally convex spaces which are generated by a weakly compact subset (or a sequence of weakly compact subsets) and their subspaces are studied. Various characterizations and the permanence properties of these spaces are obtained. Certain results valid for weakly compactly generated Banach spaces are extended. These spaces are shown to have sequential properties which extend well-known properties of separable locally convex spaces.

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

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