Factorisation in nest algebras
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- by M. Anoussis and E. G. Katsoulis PDF
- Proc. Amer. Math. Soc. 125 (1997), 87-92 Request permission
Abstract:
We give a necessary and sufficient condition on an operator $A$ for the existence of an operator $B$ in the nest algebra $\operatorname {Alg}N$ of a continuous nest $N$ satisfying $AA^*=BB^*$ (resp. $A^*A=B^*B)$. We also characterise the operators $A$ in $B(H)$ which have the following property: For every continuous nest $N$ there exists an operator $B_N$ in $\operatorname {Alg}N$ satisfying $AA^*=B_NB_N^*$ (resp. $A^*A=B_N^*B_N)$.References
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Additional Information
- M. Anoussis
- Affiliation: Department of Mathematics, University of the Aegean, Karlovassi 83200, Greece
- E. G. Katsoulis
- Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
- MR Author ID: 99165
- Received by editor(s): December 6, 1994
- Received by editor(s) in revised form: April 5, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 87-92
- MSC (1991): Primary 47D25
- DOI: https://doi.org/10.1090/S0002-9939-97-03430-8
- MathSciNet review: 1340374