|
Expanding a band
Author(s):
Gordon
MacDonald
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2625-2632.
MSC (1991):
Primary 20M20, 47D03;
Secondary 47A15
Posted:
April 23, 1999
MathSciNet review:
1610745
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Any pure operator band can be expanded so that each component of the band is reflexive.
References:
- 1.
- R. Drnov[??]sek, An irreducible semigroup of idempotents, Studia Math. 125 (1997), 97-99. MR 98e:47011
- 2.
- P. Fillmore, G. MacDonald, M. Radjabalipour and H. Radjavi, Towards a classification of maximal unicellular pure bands, Semigroup Forum 49 (1994), 195-215. MR 95f:47059
- 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.
- M. Petrich, Lectures in Semigroups, Berlin:Academie-Verlag/John Wiley & Sons Ltd., 1977. MR 56:5749; MR 57:6150
- 7.
- H. Radjavi, On the reduction and triangularization of semigroups of operators, J. Operator Theory 13 (1985), 65-71. MR 86c:47056
- 8.
- A. Loginov and V. Sulman, hereditary and intermediate reflexivity of W
 -algebras, Izv. Akad. Nauk SSSR, 39 (1975), 1260-1273; USSR-Isv., 9 (1975). MR 53:8919
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:
10.1090/S0002-9939-99-04932-1
PII:
S 0002-9939(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
Posted:
April 23, 1999
Additional Notes:
The author thanks NSERC Canada for their support.
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1999,
American Mathematical Society
|
