Bands in lattices of operators
HTML articles powered by AMS MathViewer
- by C. B. Huijsmans and A. W. Wickstead PDF
- Proc. Amer. Math. Soc. 124 (1996), 3835-3841 Request permission
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
- Ju. A. Abramovič, The maximal normed extension of partially ordered normed spaces, Vestnik Leningrad. Univ. 25 (1970), no. 1, 7–17 (Russian, with English summary). MR 0278035
- Y. A. Abramovich, Private Communication.
- Charalambos D. Aliprantis and Owen Burkinshaw, Positive operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985. MR 809372
- W. Arendt and D. R. Hart, The spectrum of quasi-invertible disjointness preserving operators, J. Funct. Anal. 68 (1986), no. 2, 149–167. MR 852658, DOI 10.1016/0022-1236(86)90003-0
- S. J. Bernau, C. B. Huijsmans, and B. de Pagter, Sums of lattice homomorphisms, Proc. Amer. Math. Soc. 115 (1992), no. 1, 151–156. MR 1086322, DOI 10.1090/S0002-9939-1992-1086322-8
- C. B. Huijsmans and B. de Pagter, Disjointness preserving and diffuse operators, Compositio Math. 79 (1991), no. 3, 351–374. MR 1121143
- Ulrich Krengel, Remark on the modulus of compact operators, Bull. Amer. Math. Soc. 72 (1966), 132–133. MR 190752, DOI 10.1090/S0002-9904-1966-11452-0
- Peter Meyer-Nieberg, Banach lattices, Universitext, Springer-Verlag, Berlin, 1991. MR 1128093, DOI 10.1007/978-3-642-76724-1
- Jürgen Voigt, The projection onto the center of operators in a Banach lattice, Math. Z. 199 (1988), no. 1, 115–117. MR 954756, DOI 10.1007/BF01160214
- A. C. Zaanen, Riesz spaces. II, North-Holland Mathematical Library, vol. 30, North-Holland Publishing Co., Amsterdam, 1983. MR 704021, DOI 10.1016/S0924-6509(08)70234-4
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
- MR Author ID: 182585
- Email: a.wickstead@qub.ac.uk
- 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 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3835-3841
- MSC (1991): Primary 47B65, 46B42
- DOI: https://doi.org/10.1090/S0002-9939-96-03547-2
- MathSciNet review: 1346978