Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Expanding a band


Author: Gordon MacDonald
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
Published electronically: April 23, 1999
MathSciNet review: 1610745
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Any pure operator band can be expanded so that each component of the band is reflexive.


References [Enhancements On Off] (What's this?)

  • 1. Roman Drnovšek, An irreducible semigroup of idempotents, Studia Math. 125 (1997), no. 1, 97–99. MR 1455626
  • 2. 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, https://doi.org/10.1007/BF02573484
  • 3. P. Fillmore, G. MacDonald, M. Radjabalipour and H. Radjavi, Principal-Ideal Bands, Semigroup Forum, to appear.
  • 4. L. Livshits, G. MacDonald, B. Mathes and H. Radjavi, Reducible semigroups of idempotent operators, J. Operator Theory, 40 (1998), 35-69.
  • 5. L. Livshits, G. MacDonald, B. Mathes and H. Radjavi, Do bands have non-trivial irreducible representations?, submitted for publication.
  • 6. Mario Petrich, Lectures in semigroups, Akademie-Verlag, Berlin, 1977. Mathematische Lehrbücher und Monographien. I. Abteilung: Mathematische Lehrbücher, Band 29. MR 0447437
    Mario Petrich, Lectures in semigroups, John Wiley & Sons, London-New York-Sydney, 1977. MR 0466270
  • 7. Heydar Radjavi, On the reduction and triangularization of semigroups of operators, J. Operator Theory 13 (1985), no. 1, 63–71. MR 768302
  • 8. 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20M20, 47D03, 47A15

Retrieve articles in all journals with MSC (1991): 20M20, 47D03, 47A15


Additional Information

Gordon MacDonald
Affiliation: Department of Mathematics and Computer Science, University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada C1A 4P3
Email: gmacdonald@upei.ca

DOI: https://doi.org/10.1090/S0002-9939-99-04932-1
Keywords: Semigroup, idempotent, band, reducible, reflexive
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
Article copyright: © Copyright 1999 American Mathematical Society