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On  -reflexive representations of algebras
Author(s):
K.
R.
Fuller;
W.
K.
Nicholson;
J.
F.
Watters
Journal:
Proc. Amer. Math. Soc.
125
(1997),
47-50.
MSC (1991):
Primary 16P10;
Secondary 47D15
MathSciNet review:
1363461
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Abstract:
Module theoretic methods are employed to obtain simple proofs of extensions of two theorems of E. A. Azoff regarding the reflexivity of direct sums of copies of an algebra of operators on a finite dimensional Hilbert space.
References:
- [1]
- F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Springer-Verlag, New York, Berlin, etc. 1992. MR 94i:16001
- [2]
- E. A. Azoff,
 -reflexivity in finite dimensional spaces, Duke Math. J. 40 (1973), 821-830. MR 48:9415 - [3]
- -, On finite rank operators and preannihilators, Mem. Amer. Math. Soc. 357 (1986). MR 88a:47041
- [4]
- J. A. Deddens and P. A. Fillmore, Reflexive linear transformations, Linear Algebra and Appl. 10 (1975), 89-93. MR 50:10856
- [5]
- L. Ding, Separating vectors and reflexivity, Linear Algebra and Appl. 174 (1992), 37-52. MR 94a:47075
- [6]
- K. R. Fuller, W. K. Nicholson and J. F. Watters, Reflexive bimodules, Canadian J. Math. 41 (1989), 592-611. MR 90g:16019
- [7]
- -, Universally reflexive algebras, Linear Algebra and Appl. 157 (1991), 195-201. MR 92g:16009
- [8]
- -, Algebras whose projective modules are reflexive, J. Pure and Appl. Algebra 98 (1995), 135-150. MR 96c:16008
- [9]
- D. Hadwin, Algebraically reflexive linear transformations, Linear and Multilin. Alg. 14 (1983), 225-233. MR 85e:47003
- [10]
- P. R. Halmos, Reflexive lattices of subspaces, J. London Math. Soc. 4 (1971), 257-263. MR 44:5808
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Additional Information:
K.
R.
Fuller
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
kfuller@math.uiowa.edu
W.
K.
Nicholson
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Email:
wknichol@math.ucalgary.ca
J.
F.
Watters
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, Leicester, England Le1 7RH
Email:
jfw@leicester.ac.uk
DOI:
10.1090/S0002-9939-97-03666-6
PII:
S 0002-9939(97)03666-6
Received by editor(s):
July 14, 1995
Additional Notes:
This research was supported by NATO Collaborative Research Grant 920159 and NSERC Grant A 8075
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1997,
American Mathematical Society
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