Banach spaces whose duals are L1 spaces and their representing matrices

Lazar, Aldo J.; Lindenstrauss, Joram

doi:10.1007/bf02392030

Cited by 129 publications

(98 citation statements)

References 17 publications

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“…Add CQ as above. By [3] Theorem 3.1. there is ^ ^ E <= A(S) with E c: E and int {\\x -y\\ | y e E} ^ s\\x\\ for all x e F . Hence E is positively generated by a peaked partition of unity {fo,fi, .…”

Section: Are Smooth Points Of A(s) Then There Is An Isometric Isomormentioning

confidence: 88%

A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld

Lusky¹

1978

Annales De L’institut Fourier

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Section: Are Smooth Points Of A(s) Then There Is An Isometric Isomormentioning

confidence: 88%

A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld

Lusky¹

1978

Annales De L’institut Fourier

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“…The facial structure of the dual unit ball of real Lindenstrauss spaces has been studied by several authors, for example Alfsen and Effros [2], Effros [7], Lau [15] and Lazar and Lindenstrauss [16]. Uttersrud [23] has given a characterization of real Lindenstrauss spaces in terms of decomposability of L-ideals in the dual space.…”

Section: Now If X G E We Have H(x)tp(x) G T 1 If X Is Not In E Then mentioning

confidence: 99%

Facial characterizations of complex Lindenstrauss spaces

Ellis¹,

Rao²,

Roy³

et al. 1981

Trans. Amer. Math. Soc.

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Abstract. We characterize complex Banach spaces A whose Banach dual spaces are £'(/*) spaces in terms of L-ideals generated by certain extremal subsets of the closed unit ball K of A*. Our treatment covers the case of spaces A containing constant functions and also spaces not containing constants. Separable spaces are characterized in terms of w*-compact sets of extreme points of K, whereas the nonseparable spaces necessitate usage of the w'-closed faces of K. Our results represent natural extensions of known characterizations of Choquet simplexes. We obtain also a characterization of complex Lindenstrauss spaces in terms of boundary annihilating measures, and this leads to a characterization of the closed subalgebras of C^X) which are complex Lindenstrauss spaces.

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“…Remarquons que ce théorème peut être démontré diffé-remment; il suffit en effet, d'après [10], de montrer que toute famille de 4 boules fermées de Jf qui se rencontrent deux à deux admet une intersection non vide. Ce fait peut être établi en construisant une sélection linéaire continue pour une application multivoque définie sur B(V) [9]. Dans le cas où V est un espace simplicial (resp.…”

Section: Propriétés Des Espacesunclassified

Approximation par des opérateurs compacts ou faiblement compacts à valeurs dans $C(X)$

Fakhoury¹

1977

Annales De L’institut Fourier

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Banach spaces whose duals are L1 spaces and their representing matrices

Cited by 129 publications

References 17 publications

A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld

A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld

Facial characterizations of complex Lindenstrauss spaces

Approximation par des opérateurs compacts ou faiblement compacts à valeurs dans $C(X)$

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