BANDS IN LATTICES OF OPERATORS

Authors
HUIJSMANS CB WICKSTEAD AW
Citation
Cb. Huijsmans et Aw. Wickstead, BANDS IN LATTICES OF OPERATORS, Proceedings of the American Mathematical Society, 124(12), 1996, pp. 3835-3841
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
124
Issue
12
Year of publication
1996
Pages
3835 - 3841
Database
ISI
SICI code
0002-9939(1996)124:12<3835:BILOO>2.0.ZU;2-2
Abstract
We consider the lattice of regular operators on a Dedekind complete Ba nach lattice. We show that in general the projection onto a band gener ated by a lattice homomorphism need not be continuous and that the pri ncipal bands need not be closed for the operator norm. In fact it is p ossible to find a convergent sequence of operators air the members of which are disjoint from the limit.