Expanding a band
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- by Gordon MacDonald PDF
- Proc. Amer. Math. Soc. 127 (1999), 2625-2632 Request permission
Abstract:
Any pure operator band can be expanded so that each component of the band is reflexive.References
- Roman Drnovšek, An irreducible semigroup of idempotents, Studia Math. 125 (1997), no. 1, 97–99. MR 1455626, DOI 10.4064/sm-125-1-97-99
- P. Fillmore, G. MacDonald, M. Radjabalipour, and H. Radjavi, Towards a classification of maximal unicellular bands, Semigroup Forum 49 (1994), no. 2, 195–215. MR 1283128, DOI 10.1007/BF02573484
- P. Fillmore, G. MacDonald, M. Radjabalipour and H. Radjavi, Principal-Ideal Bands, Semigroup Forum, to appear.
- L. Livshits, G. MacDonald, B. Mathes and H. Radjavi, Reducible semigroups of idempotent operators, J. Operator Theory, 40 (1998), 35–69.
- L. Livshits, G. MacDonald, B. Mathes and H. Radjavi, Do bands have non-trivial irreducible representations?, submitted for publication.
- Mario Petrich, Lectures in semigroups, Mathematische Lehrbücher und Monographien, I. Abteilung: Mathematische Lehrbücher, Band 29, Akademie-Verlag, Berlin, 1977. MR 0447437
- Heydar Radjavi, On the reduction and triangularization of semigroups of operators, J. Operator Theory 13 (1985), no. 1, 63–71. MR 768302
- A. N. Loginov and V. S. Šul′man, Hereditary and intermediate reflexivity of $W^*$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 6, 1260–1273, 1437 (Russian). MR 0405124
Additional Information
- Gordon MacDonald
- Affiliation: Department of Mathematics and Computer Science, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3
- MR Author ID: 271014
- Email: gmacdonald@upei.ca
- Received by editor(s): March 12, 1997
- Received by editor(s) in revised form: December 2, 1997
- Published electronically: April 23, 1999
- Additional Notes: The author thanks NSERC Canada for their support.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2625-2632
- MSC (1991): Primary 20M20, 47D03; Secondary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-99-04932-1
- MathSciNet review: 1610745