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Bands in lattices of operators
Author(s):
C.
B.
Huijsmans;
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.
References:
- [1]
- Y. A. Abramovich, On the maximal normed extension of the semi-ordered spaces, Vestnik Leningr. Univ. Mat. Meh. Astronom. 1970, no. 1, 7-17; English transl., Vestnik Leningrad Univ. Math. 3 (1976), 1-12. MR 43:3767
- [2]
- Y. A. Abramovich, Private Communication.
- [3]
- C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York & London, 1985. MR 87h:47086
- [4]
- W. Arendt and D. R. Hart, The spectrum of quasi-invertible disjointness preserving operators, J. Funct. Anal. 68 (1986), 149-167. MR 87j:47051
- [5]
- S. J. Bernau, C. B.Huijsmans and B. de Pagter, Sums of lattice homomorphisms, Proc. Amer. Math. Soc. 115 (1992), 151-156. MR 92h:46009
- [6]
- C. B. Huijsmans and B. de Pagter, Disjointness preserving and diffuse operators, Compositio Math. 79 (1991), 351-374. MR 92k:47071
- [7]
- U. Krengel, Remark on the modulus of compact operators, Bull. Amer. Math. Soc. 72 (1966), 132-133. MR 32:8162
- [8]
- P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin Heidelberg New York, 1991. MR 93f:46025
- [9]
- J. Voigt, The projection onto the center of operators in a Banach lattice, Math. Z. 199 (1988), 115-117. MR 89f:47058
- [10]
- A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, New York, London, 1983. MR 86b:46001
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Additional Information:
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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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