A Banach space is said to be if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex , then dim , 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.
@article{bwmeta1.element.bwnjournal-article-smv123i2p135bwm,
author = {V. Perenczi},
title = {Hereditarily finitely decomposable Banach spaces},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {135-149},
zbl = {0874.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv123i2p135bwm}
}
Perenczi, V. Hereditarily finitely decomposable Banach spaces. Studia Mathematica, Tome 122 (1997) pp. 135-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv123i2p135bwm/
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