Geodesic
Hereditarily finitely decomposable Banach spaces
Studia Mathematica, Tome 123 (1997) no. 2, pp. 135-149

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A Banach space is said to be $HD_n$ if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of $HD_n$ spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex $HD_n$, then dim $(ℒ(X)/S(X)) ≤ n^2$, where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic division ring.
DOI : 10.4064/sm-123-2-135-149

V. Perenczi 1

1 
@article{10_4064_sm_123_2_135_149,
     author = {V. Perenczi},
     title = {Hereditarily finitely decomposable {Banach} spaces},
     journal = {Studia Mathematica},
     pages = {135--149},
     publisher = {mathdoc},
     volume = {123},
     number = {2},
     year = {1997},
     doi = {10.4064/sm-123-2-135-149},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-123-2-135-149/}
}
TY  - JOUR
AU  - V. Perenczi
TI  - Hereditarily finitely decomposable Banach spaces
JO  - Studia Mathematica
PY  - 1997
SP  - 135
EP  - 149
VL  - 123
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-123-2-135-149/
DO  - 10.4064/sm-123-2-135-149
LA  - en
ID  - 10_4064_sm_123_2_135_149
ER  - 
%0 Journal Article
%A V. Perenczi
%T Hereditarily finitely decomposable Banach spaces
%J Studia Mathematica
%D 1997
%P 135-149
%V 123
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-123-2-135-149/
%R 10.4064/sm-123-2-135-149
%G en
%F 10_4064_sm_123_2_135_149
V. Perenczi. Hereditarily finitely decomposable Banach spaces. Studia Mathematica, Tome 123 (1997) no. 2, pp. 135-149. doi: 10.4064/sm-123-2-135-149

Cité par Sources :