# On Banach spaces which are M-ideals in their biduals.

Extracta Mathematicae (1990)

- Volume: 5, Issue: 2, page 74-76
- ISSN: 0213-8743

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topCabello Piñar, Juan Carlos. "On Banach spaces which are M-ideals in their biduals.." Extracta Mathematicae 5.2 (1990): 74-76. <http://eudml.org/doc/39875>.

@article{CabelloPiñar1990,

abstract = {A Banach space X is an M-ideal in its bidual if the relation ||f + w|| = ||f|| + ||w||holds for every f in X* and every w in X ⊥.The class of the Banach spaces which are M-ideals in their biduals, in short, the class of M-embedded spaces, has been carefully investigated, in particular by A. Lima, G. Godefroy and the West Berlin School. The spaces c0(I) -I any set- equipped with their canonical norm belong to this class, which also contains e.g. certain spaces K(E,F) of compact operators between reflexive spaces (see [7]). This class has very nice properties; for instance, these are Weakly Compactly Generated (W.C.G.) Asplund spaces [2; Th. 3], have the property (v) [5; Th. 1] and (u) [4; Main Th.] of Pelczynski and satisfy, among other isometric properties, that every isometric isomorphism of X** is the bitranspose of an isometric isomorphism of X [6; Prop. 4.2]. The purpose of this work is to show that these properties are also true in a wider class of Banach spaces.},

author = {Cabello Piñar, Juan Carlos},

journal = {Extracta Mathematicae},

keywords = {Espacios de Banach; Ideales; Espacio bidual; Operadores compactos},

language = {eng},

number = {2},

pages = {74-76},

title = {On Banach spaces which are M-ideals in their biduals.},

url = {http://eudml.org/doc/39875},

volume = {5},

year = {1990},

}

TY - JOUR

AU - Cabello Piñar, Juan Carlos

TI - On Banach spaces which are M-ideals in their biduals.

JO - Extracta Mathematicae

PY - 1990

VL - 5

IS - 2

SP - 74

EP - 76

AB - A Banach space X is an M-ideal in its bidual if the relation ||f + w|| = ||f|| + ||w||holds for every f in X* and every w in X ⊥.The class of the Banach spaces which are M-ideals in their biduals, in short, the class of M-embedded spaces, has been carefully investigated, in particular by A. Lima, G. Godefroy and the West Berlin School. The spaces c0(I) -I any set- equipped with their canonical norm belong to this class, which also contains e.g. certain spaces K(E,F) of compact operators between reflexive spaces (see [7]). This class has very nice properties; for instance, these are Weakly Compactly Generated (W.C.G.) Asplund spaces [2; Th. 3], have the property (v) [5; Th. 1] and (u) [4; Main Th.] of Pelczynski and satisfy, among other isometric properties, that every isometric isomorphism of X** is the bitranspose of an isometric isomorphism of X [6; Prop. 4.2]. The purpose of this work is to show that these properties are also true in a wider class of Banach spaces.

LA - eng

KW - Espacios de Banach; Ideales; Espacio bidual; Operadores compactos

UR - http://eudml.org/doc/39875

ER -

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