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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bands in lattices of operators


Authors: C. B. Huijsmans and A. W. Wickstead
Journal: Proc. Amer. Math. Soc. 124 (1996), 3835-3841
MSC (1991): Primary 47B65, 46B42
MathSciNet review: 1346978
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Abstract: We consider the lattice of regular operators on a Dedekind complete Banach lattice. We show that in general the projection onto a band generated by a lattice homomorphism need not be continuous and that the principal bands need not be closed for the operator norm. In fact it is possible to find a convergent sequence of operators all the members of which are disjoint from the limit.


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C. B. Huijsmans
Affiliation: Mathematisch Instituut, Rijksuniversiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
Email: chuijsmans@rulcri.leidenuniv.nl

A. W. Wickstead
Affiliation: Department of Pure Mathematics, The Queen’s University of Belfast, Belfast BT7 1NN, Northern Ireland
Email: a.wickstead@qub.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03547-2
PII: S 0002-9939(96)03547-2
Keywords: Banach lattices, positive operators, bands, norm-closed
Received by editor(s): April 19, 1995
Received by editor(s) in revised form: June 26, 1995
Additional Notes: This work was done whilst the second author was visiting Rijks Universiteit Leiden in the Summer of 1994 under the auspices of British Council/NWO Joint Scientific Research Project JRP131.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society