On -reflexive representations of algebras

Authors:
K. R. Fuller, W. K. Nicholson and J. F. Watters

Journal:
Proc. Amer. Math. Soc. **125** (1997), 47-50

MSC (1991):
Primary 16P10; Secondary 47D15

DOI:
https://doi.org/10.1090/S0002-9939-97-03666-6

MathSciNet review:
1363461

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
16P10,
47D15

Retrieve articles in all journals with MSC (1991): 16P10, 47D15

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:
https://doi.org/10.1090/S0002-9939-97-03666-6

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

Article copyright:
© Copyright 1997
American Mathematical Society