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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Factorisation in nest algebras


Authors: M. Anoussis and E. G. Katsoulis
Journal: Proc. Amer. Math. Soc. 125 (1997), 87-92
MSC (1991): Primary 47D25
MathSciNet review: 1340374
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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. $A^*A=B_N^*B_N)$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03430-8
PII: S 0002-9939(97)03430-8
Received by editor(s): December 6, 1994
Received by editor(s) in revised form: April 5, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society