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

Cabello 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 -