|
Elementary operators and invariant subalgebras
Author(s):
Keith
J.
Coates
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3437-3441.
MSC (1991):
Primary 47D25;
Secondary 47A15
MathSciNet review:
1343685
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We provide an example of an elementary operator which leaves invariant a nest algebra but which cannot be written as a finite sum of multiplications each of which leaves the nest algebra invariant. We also prove that the given operator lies in the completely bounded norm closure of the linear span of the multiplications which leave the nest algebra invariant.
References:
- [AF]
- C. Apostol and L. A. Fialkow, Structural properties of elementary operators, Can. J. Math. 38 (1986), 1485--1524. MR 88c:47071
- [CSi]
- A. Chatterjee and A. M. Sinclair, An isometry from the Haagerup tensor product into the completely bounded operators, J.Operator Theory 28 (1992), 65--78. MR 95j:46065
- [ChrSi]
- E. Christensen and A. M. Sinclair, A survey of completely bounded operators, Bull. London Math. Soc. 21 (1989), 417--448. MR 91b:46051
- [Co]
- K. Coates, Elementary operators and subalgebras, Algebraic Methods in Operator Theory, Birkhauser, Boston, 1994, pp. 49--51. MR 96b:47039
- [Cu]
- R. E. Curto, Spectral theory of elementary operators, Elementary Operators and Applications, World Scientific, 1992, pp. 3--52. MR 93i:47041
- [F]
- L. A. Fialkow, The range inclusion problem for elementary operators, Michigan Math. J. 34 (1987), 451--459. MR 89a:47052
- [KL]
- J. Kraus and D. Larson, Reflexivity and distance formulae, Proc. London Math. Soc. 53 (1986), 340--356. MR 87m:47100
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
47D25,
47A15
Retrieve articles in all Journals with
MSC (1991):
47D25,
47A15
Additional Information:
Keith
J.
Coates
Affiliation:
Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois 61702
Email:
kcoates@sun.iwu.edu
DOI:
10.1090/S0002-9939-96-03481-8
PII:
S 0002-9939(96)03481-8
Received by editor(s):
September 8, 1994
Received by editor(s) in revised form:
May 18, 1995
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
|
