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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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  • 1. W. B. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), 208-233. MR 52:3979
  • 2. J. B. Conway, A course in functional analysis, Springer-Verlag, 1985. MR 86h:46001
  • 3. K. R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, 191 (1988). MR 90f:47062
  • 4. J. Dixmier, Etude sur les variétés et les opérateurs de Julia, Bull. Soc. Math. France 77 (1949), 11-101. MR 11:369f
  • 5. R. G. Douglas, On majorization, factorization and range inclusion of operators in Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-416. MR 34:3315
  • 6. P. A. Fillmore and J. P. Williams, On operator ranges, Advances in Math. 7 (1971), 254-281. MR 45:2518
  • 7. C. Foias, Invariant para-closed subspaces, Indiana Univ. Math. J. 21 (1972), 887-906. MR 53:3734
  • 8. I.C. Gohberg and M. G. Krein, Theory and applications of Volterra operators in Hilbert space, Transl. Math. Monographs, 24 (1970), AMS. MR 41:9041
  • 9. D. R. Larson, Nest algebras and similarity transformations, Ann. of Math. 121 (1985), 409-427. MR 86j:47061
  • 10. D. R. Pitts, Factorization problems for nests: Factorization methods and characterizations of the universal factorization property, J. Funct. Ana. 79 (1988), 57-90. MR 90a:46160
  • 11. S. C. Power, Nuclear operators in nest algebras, J. Operator Theory 10 (1983), 337-352. MR 85b:47028
  • 12. S. C. Power, Factorisation in analytic operator algebras, J. Funct. Anal. 67 (1986), 413-432. MR 87k:47040
  • 13. A. L. Shields, An analogue of a Hardy-Littlewood-Fejer inequality for upper triangular trace class operators, Math. Z. 182 (1983), 473-484. MR 85c:47022

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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

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

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